In this note, a high-order disturbance observer for a class of underactuated robotic systems with mismatched uncertainties is proposed. To improve its estimation performance, a choice method of optimal gain matrices of the high-order disturbance observer is obtained as the solution of an optimization problem. A high-order disturbance observer based sliding mode control method is also designed for this class of underactuated robotic system with mismatched disturbance. The stabilities of both the disturbance observer and the controlled closed-loop system are proved by the Lyapunov theorem. Simulations on a benchmark Acrobot system demonstrate the efficiency of proposed approaches.