This study explores the optimum design of secondary optical element (SOE) for a non-coplanar two-reflector solar concentrator. The non-coplanar solar concentrator comprises a primary parabolic mirror and a secondary hyperbolic mirror. Ray tracing simulation is adopted to investigate the optical performance, including the acceptance angle and the optical efficiency, of the solar concentrator with various designs of SOE. Finally, preliminary optimum designs of SOE are presented and discussed.