Nakagami-m distribution is typically used to model various multipath fading channels in relaying networks. This work analyses a NOMA-based vehicle-to-vehicle (V2V) relaying over Nakagami-m fading channels. Specifically, we investigate the performance of a NOMA over the Nakagami-m distributed channels by leveraging a dual-hop full-duplex amplify-and-forward scheme in V2V communications. To this end, we derive closed-form expressions of rate outage probabilities and average received signal-to-interference plus noise ratios for the two vehicular users at non-identical destinations in terms of Tricomi confluent hypergeometric function. The derived analytical results are valid for arbitrary values of the fading parameter m. Furthermore, we also derive the expressions for the lower and upper bounds on rate outage probabilities. The residual self-interference, inherent in the full-duplex V2V relaying is also considered and its impact on the system’s performance is studied. The accuracy of the analytical expressions is validated by simulation results which are found to be in good agreement.