A method and apparatus are disclosed from the perspective of a UE (User Equipment). In one embodiment, the method includes transmitting a Scheduling Request (SR) on a first uplink bandwidth part (BWP). The method further includes receiving a response for the SR on a first downlink BWP. The method also includes detecting a beam failure when using the first uplink BWP and the first downlink BWP. In addition, the method includes transmitting a beam failure recovery (BFR) request to a network node on the first uplink BWP. Furthermore, the method includes receiving a control signalling on a second downlink BWP from the network node after transmitting the BFR request, wherein the control signalling is a response for the BFR request and the second downlink BWP is associated with the first uplink BWP.