Energy Efficiency (EE) is a significant problem for Cognitive Radio (CR) network. Recently, more interest has focused on EE optimization problem in wireless-powered communication. In conventional CR network, spectrum sensing and limited battery capacity may decrease system performance. In this article, a Non-Orthogonal Multiple Access (NOMA) system with Simultaneous Wireless Information and Power Transfer (SWIPT) for CR network is studied. The frame structure is designed with two subslots. In the downlink subslot, the Secondary Users (SUs) harvest wireless energy from Radio Frequency (RF) signals and sense the spectrum state simultaneously. In the uplink subslot, SUs transmit their independent information to Base Station (BS). Two modes are considered in this article: overlay network and underlay network. A CR-NOMA system model is presented and the approximate expressions of EE for two modes are obtained. Based on the subslot allocation, two optimization problems aiming to maximize EE are formulated. In the overlay network, the constraints are transmit power and total transmission slot. In the underlay network, instead of sensing the spectrum, SUs utilize the channel with primary user (PU) simultaneously. Thus, the constraints of interference threshold and channel gain of PU are also taken into considered. The proposed optimization problems can be regarded as nonlinear fractional programming. The Dinkelbach method is used to transform the nonlinear fractional programming problems into the parametric ones. Simulation results show that there indeed exists a best downlink subslot to maximize the EE of CR-NOMA networks.