diff --git a/picker_wrapper.go b/picker_wrapper.go
index bf56faa76d3d..c0e568c607cf 100644
--- a/picker_wrapper.go
+++ b/picker_wrapper.go
@@ -151,6 +151,7 @@ func (pw *pickerWrapper) pick(ctx context.Context, failfast bool, info balancer.
 		pickResult, err := p.Pick(info)
 		if err != nil {
 			if err == balancer.ErrNoSubConnAvailable {
+				lastPickErr = err
 				continue
 			}
 			if st, ok := status.FromError(err); ok {
diff --git a/picker_wrapper_test.go b/picker_wrapper_test.go
index ba99a06b0f8c..7efd0bab257f 100644
--- a/picker_wrapper_test.go
+++ b/picker_wrapper_test.go
@@ -26,6 +26,7 @@ import (
 	"time"
 
 	"google.golang.org/grpc/balancer"
+	"google.golang.org/grpc/balancer/base"
 	"google.golang.org/grpc/codes"
 	"google.golang.org/grpc/connectivity"
 	"google.golang.org/grpc/internal/transport"
@@ -74,6 +75,23 @@ func (s) TestBlockingPickTimeout(t *testing.T) {
 	}
 }
 
+func (s) TestBlockingPickErrNoSubConnAvailableTimeout(t *testing.T) {
+	bp := newPickerWrapper(nil)
+	ctx, cancel := context.WithTimeout(context.Background(), time.Millisecond)
+	defer cancel()
+
+	bp.updatePicker(base.NewErrPicker(balancer.ErrNoSubConnAvailable))
+	var err error
+	if _, _, err = bp.pick(ctx, true, balancer.PickInfo{}); status.Code(err) != codes.DeadlineExceeded {
+		t.Errorf("bp.pick returned error %v, want DeadlineExceeded", err)
+	}
+
+	serr, _ := status.FromError(err)
+	if serr.Message() != "latest balancer error: "+balancer.ErrNoSubConnAvailable.Error() {
+		t.Errorf("bp.pick returned error %v, want balancer.ErrNoSubConnAvailable", err)
+	}
+}
+
 func (s) TestBlockingPick(t *testing.T) {
 	bp := newPickerWrapper(nil)
 	// All goroutines should block because picker is nil in bp.