In this research we present design optimization methods for a vehicle-mounted satellite antenna positioner. Our initial antenna positioner was conservatively designed to satisfy a worst case scenario where wind blew across the positioner at the speed of 120 km/h. Investigating stresses and safety based on Finite Element Methods (FEM), we find reflector support frames can be optimized to significantly reduce the weight of the positioner system. Thus, we optimize the reflector support frame from the given initial design while considering weight, maximum stress, maximum allowable deflection, cross section, and thickness. As a result, Shape C and the thickness of 2 mm are determined for the cross section of the reflector support frame. Applying this result, the weight of the new antenna positioner is 57.343 kg, which is decreased by 10.74% compared to the initial conservative design.