A method and apparatus are disclosed. In an example from the perspective of a User Equipment (UE), the UE initiates a random access procedure. The UE receives a Physical Downlink Control Channel (PDCCH) transmission. The UE determines whether contention resolution associated with the random access procedure is successful. If the initiating the random access procedure is performed for Special Cell (SpCell) beam failure recovery, the determining whether the contention resolution is successful is based on whether the PDCCH transmission is addressed to a Cell Radio Network Temporary Identifier (C-RNTI) of the UE. If the initiating the random access procedure is performed for Secondary Cell (SCell) beam failure recovery, the determining whether the contention resolution is successful is based on whether the PDCCH transmission is addressed to the C-RNTI of the UE and whether the PDCCH transmission contains an uplink (UL) grant for a new transmission.