A method and apparatus are disclosed. In an example from the perspective of a User Equipment (UE), a random access procedure in a cell controlled by a network node is initiated. A downlink signal is selected from amongst configured downlink signals. A measured Reference Signal Received Power (RSRP) value associated with the downlink signal satisfies a first criterion associated with a first threshold. A measurement result associated with the downlink signal satisfies a second criterion associated with a second threshold. A random access preamble transmission of the random access procedure is performed on a Physical Random Access Channel (PRACH) occasion associated with the downlink signal.