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A numerical investigation is performed to study the effect of thermal radiation on magnetohydrodynamic (MHD) free convection flow along a vertical flat plate in presence of variable thermal conductivity in this paper. The governing equations of the flow and the boundary conditions are transformed into dimensionless form using appropriate similarity transformations and then solved employing the implicit finite difference method with Keller-box scheme. Results for the details of the velocity profiles, temperature distributions as well as the skin friction, the rate of heat transfer and surface temperature distributions are shown graphically. Results reveal that the thermal radiation is more significant in MHD natural convection flow during thermal conductivity effect is considered. To illustrate the accuracy of the present results, the results for the local skin fraction and surface temperature distribution excluding the extension effects are compared with results of Merkin and Pop designed for the fixed value of Prandtl number and a good agreement were found.