In this paper, we employ power-domain non-orthogonal multiple access (NOMA) to simultaneously transmit signals to both a primary user (PU) and a secondary user (SU) of a cognitive cooperative radio network (CCRN). Higher priority is given to the PU over the SU by keeping the power allocation coefficients at the base station (BS) and relay (R) above a certain threshold. In this way, similar as the interference power limit imposed by the PU in a conventional underlay CCRN, the power allocation coefficients at the BS and R of the CCRN can be controlled to maintain a given outage performance. Analytical expressions of the cumulative distribution function of the end-to-end signal-to-interference-plus-noise ratios at the PU and SU are derived and then used to assess the outage probabilities of both users. Numerical results are presented to study the impact of system parameters on outage performance of the CCRN with power-domain NOMA. In addition, it is illustrated that increased downlink performance can be obtained by combining power-domain NOMA with CCRNs. © 2018 IEEE.