This study investigates the steady, two-dimensional MHD (magnetohydrodynamic) free convection flow of an incompressible, viscous, and electrically conducting fluid past a vertical porous plate. The flow is subjected to a uniform transverse magnetic field acting perpendicular to the direction of flow. This study investigates the steady, two-dimensional MHD (magnetohydrodynamic) free convection flow of an incompressible, viscous, and electrically conducting fluid past a vertical porous plate. The flow is subjected to a uniform transverse magnetic field acting perpendicular to the direction of flow. The problem is governed by a coupled non-linear system of partial differential equation. In this case exact solutions are not possible, by the explicit finite difference method. The governing equations—consisting of continuity, momentum, and energy balance—are transformed into a system of non-linear ordinary differential equations using appropriate similarity variables. The velocity distribution, the temperature distribution, coefficient of skin friction and rate of heat transfer has been investigated.