The effects of magnetic force, acting vertically downward on natural convection within a porous trapezoidal enclosure saturated with an electrically conducting fluid have been investigated numerically. The bottom wall of the enclosure is subjected to a constant hot temperature and the top wall experiences a constant cold temperature whereas the remaining sidewalls are kept adiabatic. The physical problems are represented mathematically by different sets of governing equations along with the corresponding boundary conditions. By using Galerkin weighted residual method of finite element formulation, the non-dimensional governing equations are discritized. For natural convection in a porous medium the influential parameters are the modified Rayleigh number Ram, the fluid Rayleigh number Raf , the inclination angle of the sidewalls of the cavity γ, the rotational angle of the enclosure Φ and the Hartmann number Ha, through which different thermo-fluid characteristics inside the enclosure are obtained. 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 modified Rayleigh number increases. Optimum heat transfer rate is obtained at higher values of Ram in the absence of magnetic force.