Carbon fiber composite laminate has been widely used in the area of sports applications such as race car, golf club, fishing rods, yacht. In this study, carbon fiber composite laminate was used in the rear upright of leisure purposed small size single-seat electric race car to reduce its unsprung mass of suspension system. The focus of this research is to investigate in finding optimal stacking lay-up of rear upright laminated with carbon fiber composite in the early design phase. Forces transferred from circuit road to rear upright were estimated through MBD(Multi-Body Dynamics)model of the rear suspension geometry. To evaluate the strength of the rear upright laminated with carbon fiber composite which generally behaves in an anisotropic or orthotropic manner, FEA(Finite Element Analysis) model suitable for composite materials was built followed by its strength was evaluated depending on different stacking lay-up. The result showed that Symmetric stacking lay-up [45°/-45°/90°/0°]S for frontal area and symmetric stacking lay-up with 1mm aluminum core [45°/-45°/90°/Core]S for rear area were most suitable of 16 lay-up cases from the side of both strength based on Tasi-wu failure index and weight.