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In this paper, we reformulate the Vlasov-Maxwell equations based on the Morrison-Marsden-Weinstein Poisson bracket. In order to get the numerical solutions preserving the Poisson bracket, we split the Hamiltonian of the Vlasov-Maxwell equations into five parts. We construct the numerical methods for the time direction via composing the exact solutions of subsystems. By combining an appropriate spatial discretization, we can prove that the resulting numerical discretization preserves the discrete Poisson bracket. We present numerical simulations for the problems of Landau damping and two-stream stability. [ABSTRACT FROM AUTHOR]