Non-orthogonal multiple access (NOMA) and cognitive radio (CR) are envisioned as promising solutions to achieve high spectral efficiency for future wireless networks. This work investigates the outage performance of an overlay cognitive NOMA system with imperfect successive interference cancellation (SIC). The outage probability of primary user and secondary user are derived in closed forms. To obtain further insights, asymptotic expressions of outage probability and system throughput are evaluated when the transmit signal-to-noise ratio approaches infinity. An optimal power allocation coefficient is provided to maximize the system throughput. Moreover, the overlay cognitive NOMA system is compared with the underlay CR system and the overlay cognitive orthogonal multiple access (OMA) system in terms of outage probability. Finally, the performance analysis is validated by simulations. The simulation results demonstrate that the outage performance and system throughput of overlay cognitive NOMA system are superior to those of overlay cognitive OMA system and underlay CR system when the imperfect SIC satisfies certain conditions.