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In this article, an optical isolator is designed and simulated based on a hybrid configuration of the photonic crystal (PhC) and graphene. The PhC membrane is a hexagonal lattice of air holes arranged in a nonlinear silicon substrate. To provide a nonreciprocal transmission (optical isolator), breaking the symmetry of the light propagation path (the forth and back routes) is an essential condition. Here, the asymmetrical round trip of the light propagation and the Kerr-nonlinear effect are employed to obtain asymmetric propagation. The isolator structure includes a PhC waveguide that asymmetrically side-coupled to a specific embedded cavity. Then, to attain a tunable asymmetric transmission, a Nano-layer of graphene is located on the top of the mentioned PhC configuration. By altering the chemical potential of graphene one can control the isolation rate, frequency, and bandwidth of offered structure and thus possess