Security robot has gradually developed and deployed in order to protect civilian’s lives as well as fortune and subjugate the shortcomings of CCTV which lacks of mobility. We have developed a security robot for outdoor environment and the main purpose of the driving mechanism is to overcome the bumps or projections with high speed. The robot platform consists of 4 omnidirectional wheel-based driving mechanisms and suspension for each driving mechanism. In this paper, principal suspension parameters of outdoor security robot for overcoming obstacles with stability are studied and approximately optimized using Response Surface Methodology (RSM) since it is difficult to find the exact relationship between suspension parameters and the shock, which is significantly associated with stability of the robot, at the robot platform. Simulation using ADAMS is conducted for assessing the feasibility of optimized design parameters.