This paper introduces an innovative design of a multi-legged robot with switchable modes for walking and stair climbing. The Jansen-type eight-bar linkages are used as leg mechanisms with a new set of link dimensions (identified by the proposed path synthesis method) to generate foot trajectory for stair climbing motion. The objective function of the proposed path synthesis method is to minimize the tacking error between the target and generated trajectories. A counterweight slider to adjust the center of gravity of the multi-legged robot is used to switch the robot to either walking mode or stair climbing mode. The system design, and simulation results by using the commercial multibody dynamic analysis software, RecurDyn, are provided. The proposed design is prototyped, and can be remote controlled by a smartphone through Arduino and its Bluetooth module. The eight legs of the robot are driven by a dual-output-shaft DC motor through two gear trains. The simulated and experimental results show the developed robot is capable for both legged walking and stair climbing.