In this paper, the power allocation of Non-orthogonal multiple access (NOMA) for secondary users in underlay cognitive radio is studied. In underlay cognitive radio networks, the interference, which is produced by secondary users (SUs), should be less than predefined threshold. On the other hand, their SINR should be greater than certain threshold, otherwise outage occurs. Accordingly, the total rate of downlink SUs can be maximized under the SUs SINR and interference limits constraints. The optimum power allocation coefficients of users are derived. Due to the low complexity of this new method for power allocation, it can be simply implemented in the practical systems. Simulation results show that the proposed scheme achieves a higher rate and lower outage compared to the previous NOMA schemes with fixed power allocation coefficients as well as conventional orthogonal multiple access.