In recent year, embedded systems equipped with multi-core processor have been increasing to improve performance and energy saving. When tasks are executed in parallel on multi-core of embedded systems, a mechanism for mutual exclusion that maintains real-time property between cores becomes important. In this paper, we describe a mutual exclusion method using Lock-free algorithm for multi-core processor. This method has three benefits. The first is that each core can fairly acquire the lock and it is possible to determine the worst execution time. The second is that the worst execution time when increasing the number of cores is shorter than the time proportional the number of cores. The third is high CPU utilization. This has the advantage that it is possible to real-time design on a multi-core system that requires mutual exclusion. As a result of evaluation, it was possible to satisfy three requirements by the proposal method.