The wireless broadcast nature enables a video source to multicast a stream to a group of mobile clients efficiently. However, since different clients might experience heterogeneous wireless channel conditions, the throughput of single-hop multicast schemes is bounded by the clients that experience a poor channel condition. This paper presents a relay-based video multicast scheme that allows the clients experiencing a better channel condition to select a suitable transmission bit-rate and relay data for neighboring poorly-connected clients. We first formulate a joint time-allocation and rate-selection model that allocates bandwidth resources to each relay node, and then propose a network-coding-based forwarding scheme to determine which video frames should be forwarded by each relay. Our evaluation results show that the proposed relay-based scheme can utilize channel bandwidth more efficiently, and, therefore, improve the average visual quality by up to 5dB as compared to single-hop multicast.