Cognitive radio (CR) and non-orthogonal multiple access (NOMA) have been deemed two promising technologies due to their potential to achieve a high spectral efficiency and massive connectivity. In this paper, the energy efficiency (EE) is investigated in a two-way relay assisted cognitive radio non-orthogonal multiple access (CR-NOMA) network. Our objective is to maximize the EE of the SU system subject to harvested energy and the quality of service (QoS) of the users. Specifically, the multiobjective optimization problem is decomposed into three subproblems, i.e., the optimization of transmit power, power allocation, and power splitting ratio, respectively. The problem with optimizing transmit power is non-convex; hence, the Lagrange dual algorithm based on the first-order Taylor series expansion function is proposed to solve it. Besides, the multi-objective iterative algorithm (MOIA) is further proposed to achieve joint optimal solution. The simulation result shows that compared with the traditional OWR, the proposed scheme not only improves the spectral efficiency but also increases the EE of SUs by 45%. INDEX TERMS Cognitive radio, energy efficiency, NOMA, power allocation, two-way relay.