Packet multicast technology in cognitive radio ad-hoc networks (CRAN) is researched using a random network coding (RNC) based approach. A basic problem, which is termed as multi-channel single-hop wireless multicast problem (MCSHWMP), of packet multicast applications in CRAN is investigated. Definition about MCSHWMP and its 4-element tuple model were provided. A network coding based scheme framework for packet multicast applications in CRAN is described and based on which, several candidate schemes are proposed. Exploiting the broadcast nature of wireless transmissions by using RNC, necessary packet transmissions are reduced greatly. Considering opportunistic accessibility of wireless channels and heterogeneous packet reception success ratio of different wireless channels, each packet transmission is tried to maximize the packet reception gain of the receivers. Packet size to be transmitted is effectively shortened by reducing decoding information to be transmitted in the packet. Simulation results showed that, network coding based schemes can save much packet transmissions when compared with non-network coding based schemes, and the superiority of network coding based schemes is more distinctive when packet reception success ratio of wireless links is nearly but smaller than 1, in those cases, nearly 50% packet transmissions could be saved.