Device-to-device (D2D) communication is an excellent technology to improve the system capacity by sharing the spectrum resources of cellular networks. Multicast service is considered as an effective transmission mode for the future mobile social contact services. Therefore, multicast based on D2D technology can exactly improve the spectrum resource efficiency. How to apply D2D technology to support multicast service is a new issue. In this paper, a resource allocation scheme based on cognitive radio (CR) for D2D underlay multicast communication (CR-DUM) is proposed to improve system performance. In the cognitive cellular system, the D2D users as secondary users employing multicast service form a group and reuse the cellular resources to accomplish a multicast transmission. The proposed scheme includes two steps. First, a channel allocation rule aiming to reduce the interference from cellular networks to receivers in D2D multicast group is proposed. Next, to maximize the total system throughput under the condition of interference and noise impairment, we formulate an optimal transmission power allocation jointly for the cellular and D2D multicast communications. Based on the channel allocation, optimal power solution is in a closed form and achieved by searching from a finite set and the interference between cellular and D2D multicast communication is coordinated. The simulation results show that the proposed method can not only ensure the quality of services (QoS), but also improve the system throughput.