diff --git a/components/bt/bluedroid/api/include/esp_gap_ble_api.h b/components/bt/bluedroid/api/include/esp_gap_ble_api.h
index 9292f95e6..083e0beef 100644
--- a/components/bt/bluedroid/api/include/esp_gap_ble_api.h
+++ b/components/bt/bluedroid/api/include/esp_gap_ble_api.h
@@ -972,6 +972,12 @@ esp_err_t esp_ble_get_bond_device_list(int *dev_num, esp_ble_bond_dev_t *dev_lis
 
 /**
 * @brief           This function is to disconnect the physical connection of the peer device
+*                  gattc maybe have multiple virtual GATT server connections when multiple app_id registed.
+*                  esp_ble_gattc_close (esp_gatt_if_t gattc_if, uint16_t conn_id) only close one virtual GATT server connection.
+*                  if there exist other virtual GATT server connections, it does not disconnect the physical connection.
+*                  esp_ble_gap_disconnect(esp_bd_addr_t remote_device) disconnect the physical connection directly.
+*
+*
 *
 * @param[in]       remote_device : BD address of the peer device
 *
diff --git a/components/bt/bluedroid/stack/l2cap/l2c_ble.c b/components/bt/bluedroid/stack/l2cap/l2c_ble.c
index 96498b1d3..0332366d8 100644
--- a/components/bt/bluedroid/stack/l2cap/l2c_ble.c
+++ b/components/bt/bluedroid/stack/l2cap/l2c_ble.c
@@ -505,8 +505,8 @@ static BOOLEAN l2cble_start_conn_update (tL2C_LCB *p_lcb)
            up to what has been requested during connection establishement */
         if (p_lcb->conn_update_mask & L2C_BLE_NOT_DEFAULT_PARAM &&
                 /* current connection interval is greater than default min */
-                p_lcb->waiting_update_conn_min_interval > BTM_BLE_CONN_INT_MIN) {
-            /* use 7.5 ms as fast connection parameter, 0 slave latency */
+                p_lcb->current_used_conn_interval > BTM_BLE_CONN_INT_MAX_DEF) {
+            /* use 6 * 1.25 = 7.5 ms as fast connection parameter, 0 slave latency */
             min_conn_int = max_conn_int = BTM_BLE_CONN_INT_MIN;
             slave_latency = BTM_BLE_CONN_SLAVE_LATENCY_DEF;
             supervision_tout = BTM_BLE_CONN_TIMEOUT_DEF;