Abstract: In this paper, a cognitive NOMA network model based on multiple relay selection is proposed by combining NOMA technology with cognitive network. In Rayleigh fading channel, the primary network achieves reliable communication through full-duplex relay in the secondary network. In return, the secondary network is allowed to access the authorized spectrum to transmit the secondary signals. After receiving the primary and secondary signals simultaneously, the serial interference cancellation technology (SIC) is used to decode the primary and secondary signals successively, and the signals are forwarded to the primary and secondary clients according to the NOMA protocol. The cognitive NOMA network outage performance under two relay selection strategies is derived and verified by Monte Carlo simulation. The simulation results show that the two-stage relay selection strategy and full duplex technology can effectively improve the outage performance of the system.