In this paper, a new driving mechanism of security robotswhich should overcome obstacles with stability even though movingin high speed is introduced. The driving mechanism has spring-based suspension and two wheels positively necessary to overcome obstacles. From the driving mechanism, it is mainly discussed how we can decrease overshoot and impulse occurred when the robot is in the process of overcoming obstacles. Finally, design parameters of the driving mechanism which guarantees stable motion while overcoming obstacles is deduced based on simulation results. Experiments are also followed to demonstrate how well the manufactured system works in its early stage of the practical use.