Numerical solution of unsteady laminar free convection from an incompressible viscous fluid flow past a vertical cone with non-uniform surface heat flux qw(x) = axm varying as a power function of the distance from the apex of the cone (x = 0) in the presence of a transverse magnetic field applied normal to the surface is considered. The dimensionless governing coupled partial differential boundary layer equations are formulated and solved numerically using an efficient and unconditionally stable finite-difference scheme of the Crank-Nicolson type. The numerical results are validated by comparisons with previously published work and are found to be in excellent agreement. The velocity and temperature fields have been studied for various combinations of physical parameters (Prandtl number Pr, exponent and magnetic parameter M). The local as well as the average skin-friction parameter and the Nusselt number are also presented and analyzed graphically.