The control objective of a ball-balancing system is to balance a ball atop a circular arc mounted on a carriage base that can move horizontally and at the same time move the carriage to a desired position. This study designs, implements, and validates a stabilizing controller for a ball-balancing system that is nonlinear and underactuated. Moreover, the equilibrium of this system is open-loop unstable. Second-order sliding mode control is used to design the stabilizing controller. A stability analysis is conducted to show that the proposed control scheme guarantees semi-global asymptotic stability over the upper half-plane under the assumption that the ball is in contact with the arc at all times. The controller is implemented and tested on an experimental apparatus. The simulation and experimental results demonstrate the effectiveness of the proposed control scheme.