Third-order upwind finite element solutions of natural convection in a square cavity with differentially heated side walls are presented. The third-order upwind finite element scheme is developed on the basis of the Petrov-Galerkin formulation and a mixed method. A turbulent approach such as the two-equation turbulence model is not considered in the basic differential equations, used on a wide range of the Rayleigh numbers governing the dynamics of natural convection in the square cavity. Numerical compulations of natural convection flows at the Rayleigh numbers ranging from 107to 1010are achieved, and the solutions are compare to other results. Finally, the effectiveness of the third-order upwind finite element scheme to be applied to computation of natural convection problems is discussed.