This paper presents a control framework for a biped robot to maintain balance and walk on a rolling ball. The control framework consists of two primary components: a balance controller and a footstep planner. The balance controller is responsible for the balance of the whole system and combines a state-feedback controller designed by pole assignment with an observer to estimate the system's current state. A wheeled linear inverted pendulum is used as a simplified model of the robot in the controller design. Taking the output of the balance controller, namely the ideal center of pressure of the biped robot on the ball, as the input, the footstep planner computes the foot placements for the robot to track the ideal center of pressure and avoid a fall from the rolling ball. Simulation results show that the proposed controller can enable a biped robot to stably walk on balls of different sizes and rotate a ball to desired positions at desired speeds.