Optical burst switching (OBS) is a promising approach for the realization of future flexible high-speed optical networks. In particular, a multicast forwarding method for optical bursts is important if an efficient high-speed grid computing network is to be realized. In OBS networks, the number of burst replicas generated at each node is strongly restricted due to optical power impairment of multicast bursts. Moreover, unrestricted replication of multicast bursts at each OBS node may not be advantageous because an increase in the number of multicast bursts within the network causes more frequent deflection forwarding of both multicast and unicast bursts. This paper proposes an efficient hop-by-hop multicast forwarding method for optical bursts, where idle output ports are selected based on scores simply calculated using a routing table that each OBS node holds. This method can mitigate increases in loss rate and transfer delay of multicast bursts, even if the number of burst replicas generated at each OBS node is strongly restricted. Moreover, this method can efficiently mitigate an increase in the number of multicast bursts within the network by avoiding unnecessary replication of multicast bursts at each OBS node. Simulation results show that the proposed method can actually mitigate degradation of the loss rate and transfer delay for multicast bursts under the restricted number of burst replicas at each OBS node. Moreover, when the arrival rate of multicast bursts is large relative to that of unicast bursts, the proposed method is able to improve the loss rates of both multicast and unicast bursts by switching the forwarding method for the multicast bursts to the simple unicast forwarding method without burst replication.