diff --git a/internal/rootcoord/scheduler.go b/internal/rootcoord/scheduler.go
index 1f5e3d0e47..9ce202a6eb 100644
--- a/internal/rootcoord/scheduler.go
+++ b/internal/rootcoord/scheduler.go
@@ -28,6 +28,7 @@ import (
 	"github.com/milvus-io/milvus/internal/tso"
 	"github.com/milvus-io/milvus/pkg/log"
 	"github.com/milvus-io/milvus/pkg/util/lock"
+	"github.com/milvus-io/milvus/pkg/util/typeutil"
 )
 
 type IScheduler interface {
@@ -46,6 +47,7 @@ type scheduler struct {
 	tsoAllocator tso.Allocator
 
 	taskChan chan task
+	taskHeap typeutil.Heap[task]
 
 	lock sync.Mutex
 
@@ -56,16 +58,22 @@ type scheduler struct {
 	lockMapping    map[LockLevel]*lock.KeyLock[string]
 }
 
+func GetTaskHeapOrder(t task) Timestamp {
+	return t.GetTs()
+}
+
 func newScheduler(ctx context.Context, idAllocator allocator.Interface, tsoAllocator tso.Allocator) *scheduler {
 	ctx1, cancel := context.WithCancel(ctx)
 	// TODO
 	n := 1024 * 10
+	taskArr := make([]task, 0)
 	s := &scheduler{
 		ctx:            ctx1,
 		cancel:         cancel,
 		idAllocator:    idAllocator,
 		tsoAllocator:   tsoAllocator,
 		taskChan:       make(chan task, n),
+		taskHeap:       typeutil.NewObjectArrayBasedMinimumHeap[task, Timestamp](taskArr, GetTaskHeapOrder),
 		minDdlTs:       *atomic.NewUint64(0),
 		clusterLock:    lock.NewKeyLock[string](),
 		databaseLock:   lock.NewKeyLock[string](),
@@ -93,7 +101,7 @@ func (s *scheduler) Stop() {
 }
 
 func (s *scheduler) execute(task task) {
-	defer s.setMinDdlTs(task.GetTs()) // we should update ts, whatever task succeeds or not.
+	defer s.setMinDdlTs() // we should update ts, whatever task succeeds or not.
 	task.SetInQueueDuration()
 	if err := task.Prepare(task.GetCtx()); err != nil {
 		task.NotifyDone(err)
@@ -153,6 +161,7 @@ func (s *scheduler) setTs(task task) error {
 		return err
 	}
 	task.SetTs(ts)
+	s.taskHeap.Push(task)
 	return nil
 }
 
@@ -186,8 +195,14 @@ func (s *scheduler) GetMinDdlTs() Timestamp {
 	return s.minDdlTs.Load()
 }
 
-func (s *scheduler) setMinDdlTs(ts Timestamp) {
-	s.minDdlTs.Store(ts)
+func (s *scheduler) setMinDdlTs() {
+	s.lock.Lock()
+	defer s.lock.Unlock()
+
+	for s.taskHeap.Len() > 0 && s.taskHeap.Peek().IsFinished() {
+		t := s.taskHeap.Pop()
+		s.minDdlTs.Store(t.GetTs())
+	}
 }
 
 func (s *scheduler) executeTaskWithLock(task task, lockerKey LockerKey) error {
@@ -195,9 +210,12 @@ func (s *scheduler) executeTaskWithLock(task task, lockerKey LockerKey) error {
 		if err := s.setID(task); err != nil {
 			return err
 		}
+		s.lock.Lock()
 		if err := s.setTs(task); err != nil {
+			s.lock.Unlock()
 			return err
 		}
+		s.lock.Unlock()
 		s.execute(task)
 		return nil
 	}
diff --git a/internal/rootcoord/scheduler_test.go b/internal/rootcoord/scheduler_test.go
index 99c0806baf..a5f782d0dc 100644
--- a/internal/rootcoord/scheduler_test.go
+++ b/internal/rootcoord/scheduler_test.go
@@ -82,6 +82,29 @@ func newMockNormalTask() *mockNormalTask {
 	return task
 }
 
+type mockLockerKeyTask struct {
+	baseTask
+	lockerKey string
+	rw        bool
+}
+
+func (m *mockLockerKeyTask) GetLockerKey() LockerKey {
+	return NewLockerKeyChain(
+		NewClusterLockerKey(false),
+		NewDatabaseLockerKey(m.lockerKey, m.rw),
+	)
+}
+
+func newMockLockerKeyTask(lockerKey string, rw bool) *mockLockerKeyTask {
+	task := &mockLockerKeyTask{
+		baseTask:  newBaseTask(context.Background(), nil),
+		lockerKey: lockerKey,
+		rw:        rw,
+	}
+	task.SetCtx(context.Background())
+	return task
+}
+
 func Test_scheduler_Start_Stop(t *testing.T) {
 	idAlloc := newMockIDAllocator()
 	tsoAlloc := newMockTsoAllocator()
@@ -247,6 +270,87 @@ func Test_scheduler_updateDdlMinTsLoop(t *testing.T) {
 		assert.Zero(t, s.GetMinDdlTs())
 		s.Stop()
 	})
+
+	t.Run("concurrent task schedule", func(t *testing.T) {
+		idAlloc := newMockIDAllocator()
+		tsoAlloc := newMockTsoAllocator()
+		tso := atomic.NewUint64(100)
+		idAlloc.AllocOneF = func() (UniqueID, error) {
+			return 100, nil
+		}
+		tsoAlloc.GenerateTSOF = func(count uint32) (uint64, error) {
+			got := tso.Inc()
+			return got, nil
+		}
+		ctx := context.Background()
+		s := newScheduler(ctx, idAlloc, tsoAlloc)
+		paramtable.Init()
+		paramtable.Get().Save(Params.ProxyCfg.TimeTickInterval.Key, "1")
+		s.Start()
+
+		for i := 0; i < 100; i++ {
+			if s.GetMinDdlTs() > Timestamp(100) {
+				break
+			}
+			assert.True(t, i < 100)
+			time.Sleep(time.Millisecond)
+		}
+
+		w := &sync.WaitGroup{}
+		w.Add(5)
+		// locker key rw true
+		lockerKey := "hello"
+		go func() {
+			defer w.Done()
+			n := 200
+			for i := 0; i < n; i++ {
+				task := newMockLockerKeyTask(lockerKey, true)
+				err := s.AddTask(task)
+				assert.NoError(t, err)
+			}
+		}()
+
+		// locker key rw false
+		go func() {
+			defer w.Done()
+			n := 200
+			for i := 0; i < n; i++ {
+				task := newMockLockerKeyTask(lockerKey, false)
+				err := s.AddTask(task)
+				assert.NoError(t, err)
+			}
+		}()
+
+		go func() {
+			defer w.Done()
+			n := 200
+			for i := 0; i < n; i++ {
+				task := newMockLockerKeyTask(lockerKey, false)
+				err := s.AddTask(task)
+				assert.NoError(t, err)
+			}
+		}()
+
+		go func() {
+			defer w.Done()
+			n := 200
+			for i := 0; i < n; i++ {
+				task := newMockNormalTask()
+				err := s.AddTask(task)
+				assert.NoError(t, err)
+			}
+		}()
+
+		lastMin := s.GetMinDdlTs()
+		go func() {
+			defer w.Done()
+			current := s.GetMinDdlTs()
+			assert.True(t, current >= lastMin)
+			lastMin = current
+			time.Sleep(time.Millisecond * 100)
+		}()
+		w.Wait()
+	})
 }
 
 type WithLockKeyTask struct {
diff --git a/internal/rootcoord/task.go b/internal/rootcoord/task.go
index 4b0927b3bf..580a99e671 100644
--- a/internal/rootcoord/task.go
+++ b/internal/rootcoord/task.go
@@ -20,6 +20,7 @@ import (
 	"context"
 	"time"
 
+	"go.uber.org/atomic"
 	"go.uber.org/zap"
 
 	"github.com/milvus-io/milvus/pkg/log"
@@ -52,16 +53,18 @@ type task interface {
 	Execute(ctx context.Context) error
 	WaitToFinish() error
 	NotifyDone(err error)
+	IsFinished() bool
 	SetInQueueDuration()
 	GetLockerKey() LockerKey
 }
 
 type baseTask struct {
-	ctx  context.Context
-	core *Core
-	done chan error
-	ts   Timestamp
-	id   UniqueID
+	ctx        context.Context
+	core       *Core
+	done       chan error
+	isFinished *atomic.Bool
+	ts         Timestamp
+	id         UniqueID
 
 	tr       *timerecord.TimeRecorder
 	queueDur time.Duration
@@ -69,9 +72,10 @@ type baseTask struct {
 
 func newBaseTask(ctx context.Context, core *Core) baseTask {
 	b := baseTask{
-		core: core,
-		done: make(chan error, 1),
-		tr:   timerecord.NewTimeRecorderWithTrace(ctx, "new task"),
+		core:       core,
+		done:       make(chan error, 1),
+		tr:         timerecord.NewTimeRecorderWithTrace(ctx, "new task"),
+		isFinished: atomic.NewBool(false),
 	}
 	b.SetCtx(ctx)
 	return b
@@ -115,12 +119,17 @@ func (b *baseTask) WaitToFinish() error {
 
 func (b *baseTask) NotifyDone(err error) {
 	b.done <- err
+	b.isFinished.Store(true)
 }
 
 func (b *baseTask) SetInQueueDuration() {
 	b.queueDur = b.tr.ElapseSpan()
 }
 
+func (b *baseTask) IsFinished() bool {
+	return b.isFinished.Load()
+}
+
 func (b *baseTask) GetLockerKey() LockerKey {
 	return nil
 }
diff --git a/pkg/util/typeutil/heap.go b/pkg/util/typeutil/heap.go
new file mode 100644
index 0000000000..94a9ab0840
--- /dev/null
+++ b/pkg/util/typeutil/heap.go
@@ -0,0 +1,197 @@
+package typeutil
+
+import (
+	"container/heap"
+
+	"golang.org/x/exp/constraints"
+)
+
+var _ HeapInterface = (*heapArray[int])(nil)
+
+// HeapInterface is the interface that a heap must implement.
+type HeapInterface interface {
+	heap.Interface
+	Peek() interface{}
+}
+
+// Heap is a heap of E.
+// Use `golang.org/x/exp/constraints` directly if you want to change any element.
+type Heap[E any] interface {
+	// Len returns the size of the heap.
+	Len() int
+
+	// Push pushes an element onto the heap.
+	Push(x E)
+
+	// Pop returns the element at the top of the heap.
+	// Panics if the heap is empty.
+	Pop() E
+
+	// Peek returns the element at the top of the heap.
+	// Panics if the heap is empty.
+	Peek() E
+}
+
+// heapArray is a heap backed by an array.
+type heapArray[E constraints.Ordered] []E
+
+// Len returns the length of the heap.
+func (h heapArray[E]) Len() int {
+	return len(h)
+}
+
+// Less returns true if the element at index i is less than the element at index j.
+func (h heapArray[E]) Less(i, j int) bool {
+	return h[i] < h[j]
+}
+
+// Swap swaps the elements at indexes i and j.
+func (h heapArray[E]) Swap(i, j int) { h[i], h[j] = h[j], h[i] }
+
+// Push pushes the last one at len.
+func (h *heapArray[E]) Push(x interface{}) {
+	// Push and Pop use pointer receivers because they modify the slice's length,
+	// not just its contents.
+	*h = append(*h, x.(E))
+}
+
+// Pop pop the last one at len.
+func (h *heapArray[E]) Pop() interface{} {
+	old := *h
+	n := len(old)
+	x := old[n-1]
+	*h = old[0 : n-1]
+	return x
+}
+
+// Peek returns the element at the top of the heap.
+func (h *heapArray[E]) Peek() interface{} {
+	return (*h)[0]
+}
+
+type objectHeapArray[O any, E constraints.Ordered] struct {
+	objects      []O
+	getOrderFunc func(O) E
+}
+
+func (h *objectHeapArray[O, E]) Len() int {
+	return len(h.objects)
+}
+
+func (h *objectHeapArray[O, E]) Less(i, j int) bool {
+	return h.getOrderFunc(h.objects[i]) < h.getOrderFunc(h.objects[j])
+}
+
+func (h *objectHeapArray[O, E]) Swap(i, j int) {
+	h.objects[i], h.objects[j] = h.objects[j], h.objects[i]
+}
+
+func (h *objectHeapArray[O, E]) Push(x interface{}) {
+	h.objects = append(h.objects, x.(O))
+}
+
+func (h *objectHeapArray[O, E]) Pop() interface{} {
+	old := h.objects
+	n := len(old)
+	x := old[n-1]
+	h.objects = old[0 : n-1]
+	return x
+}
+
+func (h *objectHeapArray[O, E]) Peek() interface{} {
+	return h.objects[0]
+}
+
+// reverseOrderedInterface is a heap base interface that reverses the order of the elements.
+type reverseOrderedInterface[E constraints.Ordered] struct {
+	HeapInterface
+}
+
+// Less returns true if the element at index j is less than the element at index i.
+func (r reverseOrderedInterface[E]) Less(i, j int) bool {
+	return r.HeapInterface.Less(j, i)
+}
+
+// NewHeap returns a new heap from a underlying representation.
+func NewHeap[E any](inner HeapInterface) Heap[E] {
+	return &heapImpl[E, HeapInterface]{
+		inner: inner,
+	}
+}
+
+// NewArrayBasedMaximumHeap returns a new maximum heap.
+func NewArrayBasedMaximumHeap[E constraints.Ordered](initial []E) Heap[E] {
+	ha := heapArray[E](initial)
+	reverse := reverseOrderedInterface[E]{
+		HeapInterface: &ha,
+	}
+	heap.Init(reverse)
+	return &heapImpl[E, reverseOrderedInterface[E]]{
+		inner: reverse,
+	}
+}
+
+// NewArrayBasedMinimumHeap returns a new minimum heap.
+func NewArrayBasedMinimumHeap[E constraints.Ordered](initial []E) Heap[E] {
+	ha := heapArray[E](initial)
+	heap.Init(&ha)
+	return &heapImpl[E, *heapArray[E]]{
+		inner: &ha,
+	}
+}
+
+func NewObjectArrayBasedMaximumHeap[O any, E constraints.Ordered](initial []O, getOrderFunc func(O) E) Heap[O] {
+	if initial == nil {
+		initial = make([]O, 0)
+	}
+	ha := &objectHeapArray[O, E]{
+		objects:      initial,
+		getOrderFunc: getOrderFunc,
+	}
+	reverse := reverseOrderedInterface[E]{
+		HeapInterface: ha,
+	}
+	heap.Init(reverse)
+	return &heapImpl[O, reverseOrderedInterface[E]]{
+		inner: reverse,
+	}
+}
+
+func NewObjectArrayBasedMinimumHeap[O any, E constraints.Ordered](initial []O, getOrderFunc func(O) E) Heap[O] {
+	if initial == nil {
+		initial = make([]O, 0)
+	}
+	ha := &objectHeapArray[O, E]{
+		objects:      initial,
+		getOrderFunc: getOrderFunc,
+	}
+	heap.Init(ha)
+	return &heapImpl[O, *objectHeapArray[O, E]]{
+		inner: ha,
+	}
+}
+
+// heapImpl is a min-heap of E.
+type heapImpl[E any, H HeapInterface] struct {
+	inner H
+}
+
+// Len returns the length of the heap.
+func (h *heapImpl[E, H]) Len() int {
+	return h.inner.Len()
+}
+
+// Push pushes an element onto the heap.
+func (h *heapImpl[E, H]) Push(x E) {
+	heap.Push(h.inner, x)
+}
+
+// Pop pops an element from the heap.
+func (h *heapImpl[E, H]) Pop() E {
+	return heap.Pop(h.inner).(E)
+}
+
+// Peek returns the element at the top of the heap.
+func (h *heapImpl[E, H]) Peek() E {
+	return h.inner.Peek().(E)
+}
diff --git a/pkg/util/typeutil/heap_test.go b/pkg/util/typeutil/heap_test.go
new file mode 100644
index 0000000000..c4d6774102
--- /dev/null
+++ b/pkg/util/typeutil/heap_test.go
@@ -0,0 +1,91 @@
+package typeutil
+
+import (
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+func TestMinimumHeap(t *testing.T) {
+	h := []int{4, 5, 2}
+	heap := NewArrayBasedMinimumHeap(h)
+	assert.Equal(t, 2, heap.Peek())
+	assert.Equal(t, 3, heap.Len())
+	heap.Push(3)
+	assert.Equal(t, 2, heap.Peek())
+	assert.Equal(t, 4, heap.Len())
+	heap.Push(1)
+	assert.Equal(t, 1, heap.Peek())
+	assert.Equal(t, 5, heap.Len())
+	for i := 1; i <= 5; i++ {
+		assert.Equal(t, i, heap.Peek())
+		assert.Equal(t, i, heap.Pop())
+	}
+}
+
+func TestMaximumHeap(t *testing.T) {
+	h := []int{4, 1, 2}
+	heap := NewArrayBasedMaximumHeap(h)
+	assert.Equal(t, 4, heap.Peek())
+	assert.Equal(t, 3, heap.Len())
+	heap.Push(3)
+	assert.Equal(t, 4, heap.Peek())
+	assert.Equal(t, 4, heap.Len())
+	heap.Push(5)
+	assert.Equal(t, 5, heap.Peek())
+	assert.Equal(t, 5, heap.Len())
+	for i := 5; i >= 1; i-- {
+		assert.Equal(t, i, heap.Peek())
+		assert.Equal(t, i, heap.Pop())
+	}
+}
+
+type FooHeapObject struct {
+	value int
+}
+
+func GetFooHeapObjectOrderFunc(obj *FooHeapObject) int {
+	return obj.value
+}
+
+func TestMinimumObjectHeap(t *testing.T) {
+	h := []*FooHeapObject{
+		{value: 4},
+		{value: 5},
+		{value: 2},
+	}
+	heap := NewObjectArrayBasedMinimumHeap(h, GetFooHeapObjectOrderFunc)
+	assert.Equal(t, 2, heap.Peek().value)
+	assert.Equal(t, 3, heap.Len())
+	heap.Push(&FooHeapObject{value: 3})
+	assert.Equal(t, 2, heap.Peek().value)
+	assert.Equal(t, 4, heap.Len())
+	heap.Push(&FooHeapObject{value: 1})
+	assert.Equal(t, 1, heap.Peek().value)
+	assert.Equal(t, 5, heap.Len())
+	for i := 1; i <= 5; i++ {
+		assert.Equal(t, i, heap.Peek().value)
+		assert.Equal(t, i, heap.Pop().value)
+	}
+}
+
+func TestMaximumObjectHeap(t *testing.T) {
+	h := []*FooHeapObject{
+		{value: 4},
+		{value: 1},
+		{value: 2},
+	}
+	heap := NewObjectArrayBasedMaximumHeap(h, GetFooHeapObjectOrderFunc)
+	assert.Equal(t, 4, heap.Peek().value)
+	assert.Equal(t, 3, heap.Len())
+	heap.Push(&FooHeapObject{value: 3})
+	assert.Equal(t, 4, heap.Peek().value)
+	assert.Equal(t, 4, heap.Len())
+	heap.Push(&FooHeapObject{value: 5})
+	assert.Equal(t, 5, heap.Peek().value)
+	assert.Equal(t, 5, heap.Len())
+	for i := 5; i >= 1; i-- {
+		assert.Equal(t, i, heap.Peek().value)
+		assert.Equal(t, i, heap.Pop().value)
+	}
+}