In this talk, we study the Vlasov-Maxwell equations based on the Morrison-Marsden-Weinstein bracket. We develop Hamiltonian particle-in-cell methods for this system by employing finite element methods in space and splitting methods in time. In order to derive the semi-discrete system that possesses a discrete non-canonical Poisson structure, we present a criterion for choosing the appropriate finite element spaces. It is confirmed that some conforming elements, e.g., Nedelec’s mixed elements, satisfy this requirement. When the Hamiltonian splitting method is used to discretize this semi-discrete system in time, the resulting algorithm is explicit and preserves the discrete Poisson structure. Some numerical experiments have been performed with help of LSEC Parallel workstation.