In this paper, a downlink scenario of a non-orthogonal multiple access (NOMA) scheme with power constraint via spectrum sensing is considered. Such network provides improved outage performance and new scheme of NOMA-based cognitive radio (CR-NOMA) network are introduced. The different power allocation factors are examined subject to performance gap among these secondary NOMA users. To evaluate system performance, the exact outage probability expressions of secondary users are derived. Finally, the dissimilar performance problem in term of secondary users is illustrated via simulation, in which a power allocation scheme and the threshold rates are considered as main impacts of varying system performance. The simulation results show that the performance of CR-NOMA network can be improved significantly.