This paper presents a parallel typed walking robot which can walk in omni-direction and climb from a floor to a wall. We design a six D.O.F leg mechanism composed of three legs, which form a parallel mechanism with a base and a ground to generate arbitrary poses. Optimal design is conducted to maximize the walking space and the dexterity, which are normalized by the stroke of leg. Kinematic parameters are found to maximize the weighted optimal objectives. We design a triple parallel mechanism robot by inserting Stewart platform between the upper leg mechanism and the lower leg mechanism and examine the gaits when the robot walks on the ground and climbs from a floor to a wall. The analysis of walking space and dexterity for each gait shows that the triple parallel walking robot has a large walking space with a large stability region. We explore the possibility that the robot can climb from a floor to a wall. Investigating the gaits for the six steps proves that the robot can lift the foot up to the wall by combining the orientational walking space generated by three parallel mechanisms.