In a conventional cognitive radio (CR) network, only when the primary user’s (PU) frequency bands are sensed to be free, secondary users (SUs) can utilize these frequency band resources. Therefore, spectrum sensing (SS) can improve spectrum utilization. Spectrum sharing means that the SUs are allowed to utilize the licensed spectrum bands belonging to the PU to transmit information with PU simultaneously. Spectrum sharing performs well under the conditions that the interference to the PU is assured to be less than a certain threshold. Non-orthogonal multiple access (NOMA) has attracted considerable interests in recent years, which is seen as an important wireless access scheme for the coming 5G wireless communication system. Simultaneous wireless information and power transfer (SWIPT) is proposed as a popular technique to extend the operation duration of power-supply-limited wireless networks. The CR-NOMA is seen as a special form of the power-domain NOMA, wherein the requirements of the SU and PU are strictly met so that excellent system performance can be achieved. In this paper, a joint frame structure is described, wherein SUs first perform SWIPT for spectrum sensing and then transmit information via an overlay and underlay mode. Moreover, the optimization problem to maximize the achievable throughput for the CR network is presented to obtain the optimal sensing slot, while the total transmission power and the minimum rate requirements of the SUs are both constrained. A joint power allocation and sensing time optimizing algorithm based on dichotomy method are proposed to achieve the optimal solution. The simulation results show that there is a maximal throughput via setting an optimal sensing time for the secondary network.