A method and apparatus are disclosed. In an example from the perspective of a User Equipment (UE), the UE receives a first Radio Resource Control (RRC) message from a network node, wherein the first RRC message is indicative of a first uplink (UL) Bandwidth Part (BWP) of a cell. In response to initiation of a procedure to use a configured grant (CG) resource in RRC inactive state, the UE performs BWP switching from a second UL BWP of the cell to the first UL BWP of the cell. The UE performs, on the first UL BWP, a first UL transmission using the CG resource. In response to completion of the procedure, the UE performs BWP switching from the first UL BWP of the cell to the second UL BWP of the cell.