A body fitted method with unstructured Cartesian grids for simulating natural convection heat transfer of viscous fluid was studied.Cartesian grids were used and irregular volumes on boundary vicinity were reserved,and thus these grids were fully body fitted.Based on this method,natural convection-diffusion and the convection heat transfer with moving upper boundary in the 2-D inclined cavity were computed.The computed results are compared with those of STAR-CD and show good coincidence.