diff --git a/conn.go b/conn.go
index 221e6cf..2a5ff76 100644
--- a/conn.go
+++ b/conn.go
@@ -1163,7 +1163,8 @@ func (c *Conn) SetCloseHandler(h func(code int, text string) error) {
 	if h == nil {
 		h = func(code int, text string) error {
 			message := FormatCloseMessage(code, "")
-			if err := c.WriteControl(CloseMessage, message, time.Now().Add(writeWait)); err != nil {
+			err := c.WriteControl(CloseMessage, message, time.Now().Add(writeWait))
+			if err != nil && err != ErrCloseSent {
 				return err
 			}
 			return nil
diff --git a/conn_test.go b/conn_test.go
index 2b823dd..5b27f2f 100644
--- a/conn_test.go
+++ b/conn_test.go
@@ -477,6 +477,26 @@ func TestWriteAfterMessageWriterClose(t *testing.T) {
 	}
 }
 
+func TestWriteHandlerDoesNotReturnErrCloseSent(t *testing.T) {
+	var b1, b2 bytes.Buffer
+
+	client := newTestConn(&b2, &b1, false)
+	server := newTestConn(&b1, &b2, true)
+
+	msg := FormatCloseMessage(CloseNormalClosure, "")
+	if err := client.WriteMessage(CloseMessage, msg); err != nil {
+		t.Fatalf("unexpected error when writing close message, %v", err)
+	}
+
+	if _, _, err := server.NextReader(); !IsCloseError(err, 1000) {
+		t.Fatalf("server expects a close message, %v returned", err)
+	}
+
+	if _, _, err := client.NextReader(); !IsCloseError(err, 1000) {
+		t.Fatalf("client expects a close message, %v returned", err)
+	}
+}
+
 func TestReadLimit(t *testing.T) {
 	t.Run("Test ReadLimit is enforced", func(t *testing.T) {
 		const readLimit = 512