This paper presents a finite-time tracking control for a robot manipulator in the presence of a modeling uncertainty and an external disturbance. To solve the large chattering phenomenon that is caused by the high switching gain of the slidingmode control, a novel second-order sliding-mode controller that generates a continuous control input is designed with a robust differentiator. The finite-time stability of the closed-loop system is ensured using a constructive Lyapunov-stability analysis. Finally, a numerical simulation of the 2-Axis Pan-Tilt system is performed to verify the effectiveness of the proposed controller.