A method and a user equipment (UE) for wireless communication in a wireless communication system are provided. The method includes receiving serving-cell-configurations of a first serving cell and a second serving cell; receiving a Beam Failure Recovery (BFR) configuration including a configuration list that includes at least one configuration, the BFR configuration being used for at least the first serving cell, the at least one configuration indicating an identifier value of a Downlink Reference Signal (DL RS); performing a measurement by measuring at least one DL RS indicated by the configuration list, the measurement being associated with a measurement metric; selecting one configuration included in the configuration list after detecting beam failure in the first serving cell, the measurement metric of a DL RS indicated by the selected one configuration being greater than a threshold; transmitting a Medium Access Control-Control Element (MAC-CE) including at least one bitmap.