This paper proposes a medium access control (MAC) protocol for single-hop WDM star-coupler networks, in which the number of stations is larger than the number of channels and the stations have arbitrary distances to the star coupler. The proposed protocol has one control channel for reserving the slots of data channels and several data channels which are used to transmit traffic. This paper also suggests a scheme that accomplishes load balancing among data channels for arbitrary traffic patterns between stations. Since this load balancing scheme diminishes an influence that traffic patterns have on the performance of the proposed MAC protocol, the proposed system is appropriate for systems which have asymmetric traffic intensity between stations. Throughput and mean message delay of the MAC protocol are analyzed using a discrete time Markov process and a D/G/1 queue with batch arrivals. The numerical results show that the performance is improved as the message length increases, the maximum round-trip propagation delay decreases, and the number of data channels increases.