Summary form only given. This paper describes a novel biped walking system based on optimal foot force distribution by quadratic programming (QP). The hierarchical control system consists of a robust force controller for the supporting leg, a robust position controller for the non-supporting leg, an attitude controller for the body, and a free-leg motion planner. The attitude of the body of the biped robot is controlled using the reactive force as the input. The main result of this paper is an introduction of QP to distribute the force required by the attitude controller to each foot. The method can stabilize the attitude of the robot and the contact between the foot and the ground, in spite of the existence of the limitation of the frictional force between the foot and the ground. Also a new walking pattern generator based on an inverted pendulum model is proposed, which realizes globally stable tracking of the center of mass of the biped robot.