The joint unmanned aerial vehicle(UAV) trajectory and power allocation optimization for Non-orthogonal multiplex access (NOMA) protocol in cognitive radio network is investigated in this paper. In the considered system, the UAV node transmits data streams to multiple secondary users by using NOMA protocol under the interference constraint to the primary user. In order to maximize the sum rate of all secondary users, the UAV trajectory as well as the total transmission power and the power allocation scheme for NOMA should be carefully designed. Firstly, the optimization problem is modeled and formulated with interference and flying velocity constraints. Considering the non-convexity of the joint optimization, the alternate optimization algorithm is proposed. During the iteration procedure, the power allocation scheme is firstly solved by successive convex optimization tools with given UAV trajectory and total transmission power. Afterwards, with the help of optimal power allocation scheme, the UAV trajectory as well as the total transmission power is iterative optimized by using of Taylor series approximation. Simulation results are provided to verify the convergence and the effectiveness of the proposed algorithm as well as the effects of system parameters.