The multicast operation is a very commonly used operation in parallel applications. With the hardware supported multicast of the InfiniBand architecture (IBA), we propose a cyclic multicast scheme for fat-tree-based (m-port n-tree) InfiniBand networks. The basic concept of the proposed cyclic multicast scheme is to find the union sets of the output ports of switches in the paths between the source processing node and each destination processing node in a multicast group. Based on the union sets and the path selection scheme, the forwarding table for a given multicast group can be constructed. We implement the proposed multicast scheme along with the OpenSM multicast scheme and the unicast scheme on an m-port n-tree InfiniBand network simulator. The simulation results show that the proposed multicast scheme outperforms the unicast scheme for all simulated cases. For many-to-many and all-to-many cases, the cyclic multicast scheme outperforms the OpenSM multicast scheme. For many-to-all case, the performance of the cyclic multicast scheme is a little better than that of the OpenSM multicast scheme