Memory race record-replay is an important technology to resolve the nondeterminism of multi-core programs. Because of high hardware overhead, the existing memory race recorders based on point-to-point logging approach are difficult to be applied to the practical modern chip multiprocessors. In order to reduce the hardware overhead of point-to-point logging approach, a novel memory race recording algorithm implemented in concurrent logging strategy for chip multiprocessors adopting snoop-based cache coherence protocol is proposed. This algorithm records the current execution points of all threads concurrently when detecting a memory conflict. It extends the point-to-point memory race relationship between two threads to all threads in recording phase, reducing hardware overhead significantly. It also uses distributed logging mechanism to record memory races to reduce bandwidth overhead effectively in the premise of not increasing the memory race log. When replaying, this algorithm uses a simplified producer-consumer model and introduces a counting semaphore for each processor core to ensure deterministic replay, improving replay speed and reducing coherence bandwidth overhead. The simulation results on 8-core chip multiprocessor (CMP) system show that this concurrent recording algorithm based on point-to-point logging approach adds about 171B hardware for each processor, and records about 2.3B log per thousand memory instructions and adds less than 1.5% additional interconnection bandwidth overhead.