This paper deals with a new up-stair motion planning algorithm for a biped robot. The whole body of the humanoid can be visualized as a kinematically redundant robot, where the number of joints are more that the required degree of freedom. Based on the ZMP constraint equation, a sequential redundancy resolution algorithm is proposed, which ensures the ZMP trajectory, the planned operational motion, and additional sub-criteria such as joint limit index. The feasibility of the proposed algorithm is verified by simulating a up-stair motion if a human scaled 12-DOF biped robot.