A method and apparatus are disclosed from the perspective of a second User Equipment (UE) for performing sidelink communication. In one embodiment, the method includes the second UE being (pre-)configured with a sidelink resource pool in a carrier or cell, wherein a DRX (Discontinuous Reception) pattern is associated to the sidelink resource pool. The method also includes the second UE selecting a resource in the sidelink resource pool based on the DRX pattern, wherein a specific message becomes available for transmission in the second UE. The method further includes the second UE transmitting the specific message on the resource to a plurality of UEs comprising at least a first UE.