In this paper, we propose an efficient medium access protocol called the group slotted ALOHA protocol for an optical passive star network. In the group slotted ALOHA protocol, the nodes are assembled into transmitter and receiver groups. Each transmitter group communicates with receiver groups using TDMA scheme, and the nodes within a transmitter group communicate with the nodes within a receiver group using slotted ALOHA protocol. We can obtain higher system throughput than the original slotted ALOHA protocol by using the proposed protocol. The proposed protocol is easily applicable to the network architecture which has the transceivers with limited tunability. We examine the effect of system parameters(the number of the groups, the network multiplicity, the buffer size and the packet transmission probability) on the system performance. From the numerical analysis, we know that the proposed group slotted ALOHA protocol has better performance than the TDMA scheme and the original slotted ALOHA protocols and is suitable for application in high-speed LAN``s and MAN``s.