Cognitive radio (CR) and non-orthogonal multiple access (NOMA) are two promising technologies in the next generation wireless communication systems. The security of a NOMA CR network (CRN) is important but lacks of study. In this paper, a multiple-input single-output NOMA CRN relying on simultaneous wireless information and power transfer is studied. In order to improve the security of both the primary and secondary network, an artificial noise-aided cooperative jamming scheme is proposed. Different from the most existing works, a power minimization problem is formulated under a practical non-linear energy harvesting model. A suboptimal scheme is proposed to solve this problem based on semidefinite relaxation and successive convex approximation. Simulation results show that the proposed cooperative jamming scheme is efficient to achieve secure communication and NOMA outperforms the conventional orthogonal multiple access in terms of the power consumption.