In this paper, we investigate the secrecy performance of a downlink non-orthogonal multiple access enabled V2V communication system wherein a source vehicle communicates with two authenticated user vehicles, i.e., far user and near user, in the presence of a passive eavesdropper vehicle. Moreover, we formulate two scenarios based on the eavesdropper’s decoding capabilities; (1) Scenario I: when the eavesdropper vehicle has comparable decoding capabilities as with the authorized user vehicles, and (2) Scenario II: when the eavesdropper is entirely capable of perfectly decoding the signals from both authorized user vehicles. For such a system configuration with Scenarios I & II, we deduce the analytical expressions for the secrecy outage probability (SOP) and ergodic secrecy capacity over independent but not necessarily identically distributed double-Rayleigh fading channels. Further, to obtain insights into the secrecy diversity order for the legitimate user vehicles under Scenarios I & II, we present the asymptotic SOP analysis by taking three cases into account; (1) Case 1: when the average transmit signal-to-noise ratio approaches infinity, (2) Case 2: when the average channel gains of the user vehicles tend to infinity with fixed average channel gains corresponding to the eavesdropper, and (3) Case 3: when the average channel gains pertaining to the user vehicles and the eavesdropper tend to infinity. From which, we can infer that the secrecy diversity order of the far user vehicle is zero for Cases 1, 2, & 3, whereas the secrecy diversity order of the near user vehicle is zero for Cases 1 & 3 and one for Case 2, under Scenarios I & II. The numerical and simulation results corroborate our theoretical investigations. Our results demonstrate the impact of transmit power, power allocation factor, channel conditions of legitimate users and eavesdropper on the system’s secrecy performance.