This paper considers the unsteady mixed convective boundary layer flow of a viscous incompressible electrically conducting fluid past an accelerated infinite vertical porous flat plate with suction in presence of a transverse magnetic field. The governing equations are solved both analytically and numerically using finite difference scheme. The flow phenomenon has been characterized with the help of flow parameters such as magnetic parameter (M), suction parameter (a), porosity parameter Grashof number for heat transfer (Gr) and Prandtl number (Pr). The effects of these parameters on the velocity field, temperature field, skin friction and heat flux have been studied and the results are presented graphically and discussed quantitatively. This type of problem is very much significant in geophysical and cosmical studies.