Abstract: The numerical analysis and calculation or natural convection in porous medium within a closed trapezoidal cavity using Galerkin finite element method are investigated in this paper. The range of the calculation is from conduction state to steady convection state(Ra:5~350). The distributions of flow field and temperature field and the curve of Nusselt number versus Rayleigh number are found for the different trapezoid decline angles of 0°, 5°, 10°, 30°and 45°. The effects of initial valus of iteration, relaxation factors and numble of element on numerical results are studied in detail. It is show when trapezoid decline angle increases the heat transfer intensifies and for the very small Rayleigh numble (c1=40) the steady flow will be formed. Finally, the results of the numerical calculation are discussed and compared with the vesults using other methods.