This paper addresses a position and speed tracking problem for high-speed train automatic operation with actuator saturation and speed limit. A nonlinear model predictive control (NMPC) approach, which allows the explicit consideration of state and input constraints when formulating the problem and is shown to guarantee the stability of the closed-loop system by choosing a proper terminal cost and terminal constraints set, is proposed. In NMPC, a cost function penalizing both the train position and speed tracking error and the changes of tracking/braking forces will be minimized on-line. The effectiveness of the proposed approach is verified by numerical simulations.