Full-duplex relaying has attracted a lot of attention recently due to its capability of receiving and forwarding simultaneously in the same frequency band. However, most of the existing designs focus on unicast communication and customize the relaying algorithm so as to maximize the receiving signal strength of a particular user. In this work, we aim at developing a full-duplex constructive forwarding system for wireless multicast. As different multicast members typically have heterogeneous channel state information, it is especially challenging to find a forwarding processing strategy that works fine for all the multicast members. To overcome this issue, we propose two models, one for maximizing the worst SNR of the multicast members while the other optimizing the overall reception quality, which is especially suitable for video multicast. We evaluate our designs via trace-driven simulations. The results demonstrate that we can consistently improve the worst SNR by 2-3 dB and the gain is especially significant for a large coverage network area.