The group theoretic method is applied for solving problem of a unsteady free-convective laminar boundary-layer flow on a non-isothermal vertical plate under the effect of an external velocity and a magnetic field normal to the plate. The application of two-parameter transformation group reduces the number of independent variables, by two, and consequently the system of governing partial differential equations with the boundary and initial conditions reduces to a system of ordinary differential equations with appropriate corresponding conditions. The Runge-Kutta shooting method used to find the numerical solution of the velocity field, shear stress, heat transfer and heat flux has been obtained. The effect of the magnetic field on the velocity field and the Prandtl number on the heat transfer and heat flux has been discussed