Abstract: A relaxation magnetohydrodynamics (MHD) model is proposed for the computation of an electromagnetically driven vacuum-plasma system. It is similar to seylers proposal in adopting full electromagnetic model, but is different in adopting the relaxed generalized Ohms law (electron inertia term omitted) as a constitutive relation to close the Maxwells equations. Therefore it is the most simplified model for the concerned correlative problems (Hall term could also be included without increasing independent variables). The dispersion relation is given to show its transition from electromagnetic propagation in vacuum to resistive MHD in plasma in a natural way. The phase and group velocities are finite for this system. A better time stepping is adopted to give a 3rd full order convergence in time domain without the stiff relaxation term restriction. Therefore it is convenient for explicit parallel computations.