In underlay cognitive radio (CR) multicast networks, the cognitive base station (CBS) can transmit at the lowest rate of all the secondary users (SUs) within the multicast group. Existing works showed that the sum rate of such networks saturates when the number of SUs increases. In this letter, for CR multicast networks with multiple channels, we group the SUs into different subgroups, each with an exclusive channel. Then, the problem of joint user grouping and power allocation to maximize the sum rate of all subgroups under the interference power constraint and the transmit power constraint is investigated. Compared to exponential complexity in the number of SUs required by the optimal algorithm, we proposed an efficient algorithm with only linear complexity. Simulation results confirm that the proposed algorithm achieves the sum rate very closed to that achieved by the optimal algorithm and greatly outperforms the maximum signal-to-noise-ratio based user grouping algorithm and the conventional algorithm without user grouping.