The steady MAGNETOHYDRODYNAMIC natural convection coutte flow of viscous incompressible and electrically conducting fluid having variable electrical conductivity between two parallel plates when one of the plate is set into motion is studied. The dimensionless differential equations as well as energy equations are solved analytically using the method of undetermined coefficient. The analytical solution are presented numerically inform of line graphs given interms of velocity and skin friction. The result reveal that the effect of the Hartmann number and grashof number are to reduce and increase the velocity respectively. Similarly the skin friction on the moving and stationary plates increase with Grashof number and decreases with increase in Hartmann, a comparetive study review that the effect of Hartmann number and grashof number on velocity and skin friction are same.