The effects of an inclined magnetic field and heat generation on unsteady free convection within a square cavity filled with a fluid-saturated porous medium have been investigated numerically. The top and bottom horizontal walls of the enclosure are adiabatic whereas the vertical walls are kept at constant but different temperatures. The physical problems are represented mathematically by a set of partial differential equations along with the corresponding boundary conditions. By using an implicit finite-difference scheme, namely the ADI method (Alternative Direction Implicit), the non-dimensional governing equations are numerically solved. The influential parameters are the Rayleigh number Ra, the inclination angle gamma of the magnetic field relative to the gravity vector g, the Hartmann number Ha and the heat generation parameter Q. In the present study, the obtained results are presented in terms of streamlines, isotherms and average Nusselt number along the hot wall. The result shows that with increasing Ha, the diffusive heat transfer become prominent even though the Rayleigh number increases. (C) 2011 Elsevier Ltd. All rights reserved.