diff --git a/src/encoding/json/decode.go b/src/encoding/json/decode.go
index 407fbcedbe9..86d8a69db7e 100644
--- a/src/encoding/json/decode.go
+++ b/src/encoding/json/decode.go
@@ -773,14 +773,14 @@ func (d *decodeState) object(v reflect.Value) error {
 			kt := t.Key()
 			var kv reflect.Value
 			switch {
-			case kt.Kind() == reflect.String:
-				kv = reflect.ValueOf(key).Convert(kt)
 			case reflect.PtrTo(kt).Implements(textUnmarshalerType):
 				kv = reflect.New(kt)
 				if err := d.literalStore(item, kv, true); err != nil {
 					return err
 				}
 				kv = kv.Elem()
+			case kt.Kind() == reflect.String:
+				kv = reflect.ValueOf(key).Convert(kt)
 			default:
 				switch kt.Kind() {
 				case reflect.Int, reflect.Int8, reflect.Int16, reflect.Int32, reflect.Int64:
diff --git a/src/encoding/json/decode_test.go b/src/encoding/json/decode_test.go
index 4cbd2172d06..498bd97b46e 100644
--- a/src/encoding/json/decode_test.go
+++ b/src/encoding/json/decode_test.go
@@ -2411,3 +2411,23 @@ func TestUnmarshalRecursivePointer(t *testing.T) {
 		t.Fatal(err)
 	}
 }
+
+type textUnmarshalerString string
+
+func (m *textUnmarshalerString) UnmarshalText(text []byte) error {
+	*m = textUnmarshalerString(strings.ToLower(string(text)))
+	return nil
+}
+
+// Test unmarshal to a map, with map key is a user defined type.
+// See golang.org/issues/34437.
+func TestUnmarshalMapWithTextUnmarshalerStringKey(t *testing.T) {
+	var p map[textUnmarshalerString]string
+	if err := Unmarshal([]byte(`{"FOO": "1"}`), &p); err != nil {
+		t.Fatalf("Unmarshal unexpected error: %v", err)
+	}
+
+	if _, ok := p["foo"]; !ok {
+		t.Errorf(`Key "foo" is not existed in map: %v`, p)
+	}
+}