Cognitive radio (CR) nonorthogonal multiple access (NOMA) network (recorded as CRNOMA) is one of the research hotspots in the field of wireless communication. Due to the openness of wireless channel, the security communication of wireless network becomes an urgent problem. For the spectrum sharing multiantenna CRNOMA network, First, the secrecy outage probability (SOP) of the optimal antenna selection (OAS) scheme is analyzed, and its exact closedform expression is derived. Secondly, the SOP of spacetime transmission (STT) scheme is analyzed, and its exact closedform expression is derived. Then, the asymptotic secrecy performance of secondary user SOP is analyzed to reveal the influence of system parameters on the secrecy communication performance. Finally, the Monte Carlo simulation is used to verify the correctness of theoretical analysis. It is found that there is an optimal transmit power in the base station under two schemes, which makes the secrecy outage performance of secondary user the best. The simulation results show that increase the peak transmission power of the base station, the secrecy outage performance of close secondary user under OAS scheme is always better than that of STT scheme, the secrecy outage performance of remote secondary user will be inferior to that of STT scheme.