A shape of the satellite's solar sail membrane is essential for unloading angular momentum in the three-axis stabilized attitude control system because the three-dimensional solar sail can receive solar radiation pressure from arbitrary directions. In this paper, the objective is the shape optimization of a three-dimensional membrane-structured solar sail using the angular momentum unloading strategy. We modelled and simulated the solar radiation pressure torque, for unloading angular momentum. Using the simulation system, since the unloading angular momentum rate is maximized, the shape of the three-dimensional solar sail was optimized using a Genetic algorithm and Sequential Quadratic Programming. The unloading velocity in the optimized shaped solar sail was greatly improved with respect to a conventional flat or pyramid solar sail.