Cooperative jamming can effectively combat eavesdropping in physical layer security communication without affecting the legal receiver and improve the security performance of the system. This paper introduces cooperative jamming to cognitive radio (CR) networks with non-orthogonal multiple access (NOMA) technology. The secure performance of the considered CR and NOMA (CR-NOMA) network is evaluated using two modes: non-cooperative jamming and cooperative jamming. In particular, the secrecy outage probabilities (SOPs) of the primary user (PU) in the two modes are derived under Rician fading channels, based on which, the influences of the transmission signal-to-noise ratio (SNR) of secondary users (SUs), the number of SUs, the secrecy rate, and the power allocation coefficient on the SOPs of PU are analyzed thereafter. Both analysis and simulation results show that cooperative jamming effectively prevents eavesdropping behaviour, which reduces the SOP of PU compared to non-cooperative jamming. We also show that the transmission SNR, the number of SUs, the secrecy rate, and the power distribution coefficients greatly influence performance improvement.