diff --git a/balancer.go b/balancer.go
index 9d943fba..44db9317 100644
--- a/balancer.go
+++ b/balancer.go
@@ -385,6 +385,9 @@ func (rr *roundRobin) Notify() <-chan []Address {
 func (rr *roundRobin) Close() error {
 	rr.mu.Lock()
 	defer rr.mu.Unlock()
+	if rr.done {
+		return errBalancerClosed
+	}
 	rr.done = true
 	if rr.w != nil {
 		rr.w.Close()
diff --git a/clientconn.go b/clientconn.go
index 434cab43..41a52937 100644
--- a/clientconn.go
+++ b/clientconn.go
@@ -78,6 +78,8 @@ var (
 	errConnClosing = errors.New("grpc: the connection is closing")
 	// errConnUnavailable indicates that the connection is unavailable.
 	errConnUnavailable = errors.New("grpc: the connection is unavailable")
+	// errBalancerClosed indicates that the balancer is closed.
+	errBalancerClosed = errors.New("grpc: balancer is closed")
 	// minimum time to give a connection to complete
 	minConnectTimeout = 20 * time.Second
 )