Three-dimensional conservation equations for natural convection in a cubic enclosure heated from one side wall and cooled from an opposing wall are numerically solved under three different external magnetic fields either in the X-, Y- or Z-directions. Sample computations are carried out for Ra = 106 and 107 and Ha = 0–500 for Pr = 0.054. The external magnetic field perpendicular to the vertical boundary layer type flow is found to be most effective in suppressing the convection. However, the external magnetic field parallel to the vertical hot and cold walls is found to be least effective, although it is perpendicular to the main circulating flow along both the vertical and horizontal boundaries. When the magnetic field is relatively strengthened, for example, at Ra = 106 and Ha = 300, secondary flow is found to be doubly strengthened with a reduction in the main circulation flow.