We present a computational study for a family of discontinuous Galerkin methods for the one dimensional Vlasov-Poisson system, recently introduced in \cite{acs0}. We introduce a slight modification of the methods to allow for feasible computations while preserving the properties of the original methods. We study numerically the verification of the theoretical and convergence analysis, discussing also the conservation properties of the schemes. The methods are validated through their application to some of the benchmarks in the simulation of plasma physics.