Medium access control (MAC) protocol design for cooperative networks over multi-packet reception (MPR) channels is a challenging topic, but has not been addressed in the literature yet. In this paper, we propose a MAC protocol to exploit the cooperation diversity for throughput enhancement over MPR channels. The proposed approach can efficiently utilize the idle periods for packet relaying, and can thus effectively limit the throughput loss resulting from the relay phase. By means of a Markov chain model, the worst-case throughput analysis is conducted. Specifically, we derive (i) a closed-form upper bound for the throughput penalty of the direct link that is caused by the interference of concurrent packet relay transmission; (ii) a closed-form lower bound for the throughput gain that a user with packet transmission failure can benefit thanks to cooperative packet relaying. The results allow us to investigate the throughput performance of the proposed protocol directly in terms of the MPR channel coefficients. Simulation results confirm the system-wide throughput advantage achieved by the proposed scheme, and also validate the analytic results.