In conventional cognitive radio (CR), the users in secondary network (SN) can only access the idle spectrum when users in primary network (PN) are absent. This novel strategy provides higher spectrum efficiency when detecting the presence of the PN. Hence, spectrum utilization of the traditional scheme can be further improved as exploiting application of non-orthogonal multiple access (NOMA). As combination of CR and NOMA, such CR-NOMA has been proposed to improve spectrum efficiency to adapt to requirements in 5G communications. In this study, the relaying scheme is employed in the SN of the proposed CR-NOMA and the relay is allowed to energy harvesting (EH) from the secondary transmitter to serve signal forwarding to distant secondary users. With this regard, the complex model of EH-assisted CR-NOMA is explored in outage behavior and throughput performance as awareness on imperfect successive interference cancellation (SIC) at the receiver. As most important results, the exact closed-form of the exact outage probability is derived for each NOMA destination by assuming that the channel coefficients among considered links follow Rayleigh distribution. Furthermore, performance gap between two NOMA users can be controlled by various parameters such as transmit power, energy harvesting coefficients and levels of imperfect SIC. Simulation results verify our analytical results.