Vehicle-to-vehicle (V2V) communication appeals to increasing research interest as a result of its applications to provide safety information as well as infotainment services. The increasing demand of transmit rates and various requirements of quality of services (QoS) in vehicular communication scenarios call for the integration of V2V communication systems and potential techniques in the future wireless communications, such as full duplex (FD) and non-orthogonal multiple access (NOMA) which enhance spectral efficiency and provide massive connectivity. However, the large amount of data transmission and user connectivity give rise to the concern of security issues and personal privacy. In order to analyze the security performance of V2V communications, we introduce a cooperative NOMA V2V system model with an FD relay. This paper focuses on the security performance of the FD-NOMA based V2V system on the physical layer perspective. We first derive several analytical results of the ergodic secrecy capacity. Then, we propose a secrecy sum rate optimization scheme utilizing the instantaneous channel state information (CSI), which is formulated as a non-convex optimization problem. Based on the differential structure of the non-convex constraints, the original problem is approximated and solved by a series of convex optimization problems. Simulation results validate the analytical results and the effectiveness of the secrecy sum rate optimization algorithm.