Abstract: This paper studied the impact of relay selection scheme on the outage performance of cognitive non-orthogonal multiple access (CR-NOMA) networks. A two-stage relay selection scheme is proposed. In the first time slot, on the basis of ensuring the quality of service of the primary user, the source broadcasts the superimposed signal to the cognitive relay cluster. In the second time slot, decode and-forward (DF) protocol is used at the selected relay to assist simultaneous transmission from the source to destination users. Based on the above assumptions, the closed expression of the secondary user outage probability is derived and the analysis results are given. It is proved that the two-stage relay selection strategy can achieve better outage performance and greater diversity gain than partial relay selection strategy. At the same time, the analysis results verify the influence of the number of alternate relay nodes and the power allocation factor on the system outage performance. The Monte Carlo simulation verified the theoretical results.