diff --git a/server/grpc_service.go b/server/grpc_service.go
index 585bd434f7a..f12a2b812db 100644
--- a/server/grpc_service.go
+++ b/server/grpc_service.go
@@ -42,14 +42,18 @@ import (
 	"google.golang.org/grpc/status"
 )
 
-const slowThreshold = 5 * time.Millisecond
+const (
+	heartbeatSendTimeout = 5 * time.Second
+	slowThreshold        = 5 * time.Millisecond
+)
 
 // gRPC errors
 var (
 	// ErrNotLeader is returned when current server is not the leader and not possible to process request.
 	// TODO: work as proxy.
-	ErrNotLeader  = status.Errorf(codes.Unavailable, "not leader")
-	ErrNotStarted = status.Errorf(codes.Unavailable, "server not started")
+	ErrNotLeader            = status.Errorf(codes.Unavailable, "not leader")
+	ErrNotStarted           = status.Errorf(codes.Unavailable, "server not started")
+	ErrSendHeartbeatTimeout = status.Errorf(codes.DeadlineExceeded, "send heartbeat timeout")
 )
 
 // GetMembers implements gRPC PDServer.
@@ -458,10 +462,6 @@ func (s *Server) StoreHeartbeat(ctx context.Context, request *pdpb.StoreHeartbea
 	}, nil
 }
 
-const regionHeartbeatSendTimeout = 5 * time.Second
-
-var errSendRegionHeartbeatTimeout = errors.New("send region heartbeat timeout")
-
 // heartbeatServer wraps PD_RegionHeartbeatServer to ensure when any error
 // occurs on Send() or Recv(), both endpoints will be closed.
 type heartbeatServer struct {
@@ -481,9 +481,9 @@ func (s *heartbeatServer) Send(m *pdpb.RegionHeartbeatResponse) error {
 			atomic.StoreInt32(&s.closed, 1)
 		}
 		return errors.WithStack(err)
-	case <-time.After(regionHeartbeatSendTimeout):
+	case <-time.After(heartbeatSendTimeout):
 		atomic.StoreInt32(&s.closed, 1)
-		return errors.WithStack(errSendRegionHeartbeatTimeout)
+		return ErrSendHeartbeatTimeout
 	}
 }
 
@@ -1243,7 +1243,7 @@ func (s *Server) GetOperator(ctx context.Context, request *pdpb.GetOperatorReque
 // TODO: Call it in gRPC interceptor.
 func (s *Server) validateRequest(header *pdpb.RequestHeader) error {
 	if s.IsClosed() || !s.member.IsLeader() {
-		return errors.WithStack(ErrNotLeader)
+		return ErrNotLeader
 	}
 	if header.GetClusterId() != s.clusterID {
 		return status.Errorf(codes.FailedPrecondition, "mismatch cluster id, need %d but got %d", s.clusterID, header.GetClusterId())
@@ -1423,7 +1423,7 @@ func (s *Server) GetDCLocationInfo(ctx context.Context, request *pdpb.GetDCLocat
 // the gRPC communication between PD servers internally.
 func (s *Server) validateInternalRequest(header *pdpb.RequestHeader, onlyAllowLeader bool) error {
 	if s.IsClosed() {
-		return errors.WithStack(ErrNotStarted)
+		return ErrNotStarted
 	}
 	// If onlyAllowLeader is true, check whether the sender is PD leader.
 	if onlyAllowLeader {
diff --git a/tests/server/cluster/cluster_test.go b/tests/server/cluster/cluster_test.go
index 48dd36444f8..7e77980e083 100644
--- a/tests/server/cluster/cluster_test.go
+++ b/tests/server/cluster/cluster_test.go
@@ -39,6 +39,8 @@ import (
 	syncer "github.com/tikv/pd/server/region_syncer"
 	"github.com/tikv/pd/server/schedule/operator"
 	"github.com/tikv/pd/tests"
+	"google.golang.org/grpc/codes"
+	"google.golang.org/grpc/status"
 )
 
 func Test(t *testing.T) {
@@ -416,6 +418,25 @@ func (s *clusterTestSuite) TestGetPDMembers(c *C) {
 	c.Assert(len(resp.GetMembers()), Not(Equals), 0)
 }
 
+func (s *clusterTestSuite) TestNotLeader(c *C) {
+	tc, err := tests.NewTestCluster(s.ctx, 2)
+	defer tc.Destroy()
+	c.Assert(err, IsNil)
+	c.Assert(tc.RunInitialServers(), IsNil)
+
+	tc.WaitLeader()
+	followerServer := tc.GetServer(tc.GetFollower())
+	grpcPDClient := testutil.MustNewGrpcClient(c, followerServer.GetAddr())
+	clusterID := followerServer.GetClusterID()
+	req := &pdpb.AllocIDRequest{Header: testutil.NewRequestHeader(clusterID)}
+	resp, err := grpcPDClient.AllocID(context.Background(), req)
+	c.Assert(resp, IsNil)
+	grpcStatus, ok := status.FromError(err)
+	c.Assert(ok, IsTrue)
+	c.Assert(grpcStatus.Code(), Equals, codes.Unavailable)
+	c.Assert(grpcStatus.Message(), Equals, "not leader")
+}
+
 func (s *clusterTestSuite) TestStoreVersionChange(c *C) {
 	tc, err := tests.NewTestCluster(s.ctx, 1)
 	defer tc.Destroy()