A numerical study is performed on unsteady natural convection heat transfer and fluid flow in a cavity under reduced gravity. Consideration is given to the influences of Marangoni and buoyancy convections on the thermal and velocity fields in a two-dimensional square cell. Here, it consists of two opposing vertical side walls held at constant but different temperature with the horizontal lower wall insulated and the upper face treated as non-deformable adiabatic free surface. The governing equations are discretized by means of a finite-difference technique and numerically solved. If only the buoyancy convection is taken into account, the fluid temperature gradient in the cavity under the reduced gravity is substantially decreased near the hot and cold vertical walls and the dominant heat transfer mechanism switches from convection into conduction, as time progresses. In other words, the heat transfer performance is substantially attenuated due to the absence of buoyancy. On the contrary, the corresponding flow pattern is similar to that under normal gravity condition, resulting in a slight deterioration of the heat transfer performance, if both Marangoni and buoyancy convections interact. Therefore, this is found to be the dominance of Marangoni flow over natural convection in the system considered.