Apparatus and method for performing beam failure recovery in a wireless communication system are provided. The method performed by a User Equipment (UE) includes receiving, from a base station, a first bandwidth part (BWP) configuration corresponding to a first BWP, a second BWP configuration corresponding to a second BWP, and a BWP inactivity timer; determining whether a BFR procedure is triggered; when determining that the BFR procedure is triggered: stopping the BWP inactivity timer and performing BWP switching from the first BWP to the second BWP.