In 5G wireless communication networks, Non-Orthogonal Multiple Access (NOMA) has attracted much attention in recent years. This paper investigates physical layer security of a NOMA system with Full Duplex Relay (FDR) and Half Duplex Relay (HDR). This system consists of one eavesdropper and two legal NOMA users where a dedicated FDR (or HDR) assists far user. In order to characterize the secrecy performance of the considered scenario, new exact expressions are derived for the Secrecy Outage Probability (SOP) of both FDR and HDR systems. Monte Carlo simulations are provided to verify the derived analytical results. Simulations demonstrate that, the NOMA-FDR system attains better performance compared to the NOMA-HDR system for both users. Also, we find that far user has always poor secrecy against near user.