This study aims to achieve the smooth going up and down the step for a biped robot whose leg has 6 DOFs with kinematics redundancy. If COG position is not controlled in the going up and down motion, the robot falls down forward or backward. The robot has achieved the motion of going up the step in the proposed approach by its COG out of shifting the waist position. In our proposed approach, the COG position is moved with the waist position shifting, and then the climbing and down motions have been realized. It is also confirmed that the robot could climb and down the known height step safely and climb down the unknown height step by the waist position shifting and the COG position changing. It is found that the required COG displacements depend on the depth of the step in the case of climbing down. The relationships among the COG displacements and the depth of the step have been made clear in the experimental studies in this paper.