In this article, we develop a robust sliding-mode nonlinear predictive controller for brain-controlled robots with enhanced performance, safety, and robustness. First, the kinematics and dynamics of a mobile robot are built. After that, the proposed controller is developed by cascading a predictive controller and a smooth sliding-mode controller. The predictive controller integrates the human intention tracking with safety guarantee objectives into an optimization problem to minimize the invasion to human intention while maintaining robot safety. The smooth sliding-mode controller is designed to achieve robust desired velocity tracking. The results of human-in-the-loop simulation and robotic experiments both show the efficacy and robust performance of the proposed controller. This work provides an enabling design to enhance the future research and development of brain-controlled robots.