A two-dimensional natural convection flow of a viscous incompressible and electrically conducting fluid past a vertical impermeable flat plate is considered in presence of a uniform transverse magnetic field. Here the viscosity is taken as dependent on temperature whereas the thermal conductivity is assumed constant. We also investigate the effect of magnetic field on the natural convection flow of a viscous incompressible and electrically conducting fluid. The effect of variable viscosity and magnetic field on local skin friction, the rate of heat transfer and the profiles for velocity as well as viscosity in the entire free convection regime are presented and discussed.