This paper investigates a two dimensional hydromagnetic unsteady mixed convective flow of a viscous incompressible electrically conducting polar fluid past a semi-infinite vertical porous flat moving plate. The plate is subjected to move with a uniform velocity in the upward direction in its own plane and the free stream velocity follows an exponentially increasing or decreasing small perturbation law. The flow field is subjected to a uniform magnetic field normal to the porous surface which absorbs the polar fluid with a suction velocity varying with time. The governing equations for velocity, angular velocity and temperature of flow field have been solved employing perturbation technique. The effects of the material parameters on the flow field across the boundary layer have been analyzed with the aid of figures.