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In this paper, we focus on improving concurrent MAC (CMAC) protocol performance in multi-hop ad hoc networks. Based on the analysis of the collision problems and multi-rate problems of the distributed coordination function (DCF) and CMAC protocol in multi-hop ad hoc networks, we propose a rate adaptive scheme for improving CMAC protocol performance. The scheme allows nodes to adaptively select appropriate Data rates to avoid collisions between the concurrent Data transmissions, which makes more nodes simultaneously transmit their own Data frames successfully and thus improves the performance of CMAC protocol. Simulation results show that higher overall throughput can be obtained by our scheme in comparison with CMAC protocol.