A method and apparatus are disclosed from the perspective of a first device for performing sidelink communication. In one embodiment, the method includes the first device being configured with network scheduling mode for sidelink by a base station. The method further includes the first device being configured with a first set of resources with a first time pattern for sidelink transmission through a dedicated signaling. The method also includes the first device using the first set of resources to perform sidelink transmission when the first device does not detect beam failure. Furthermore, the method includes the first device detecting a beam failure between the first device and the base station. In addition, the method includes the first device using the first set of resources to perform sidelink transmission to a second device when the beam failure is not resolved.