Human neural motor system has the intelligence to learn new skills, and then to generalize these skills naturally. But it is not easy for a robot to demonstrate such intelligent behaviors. Inspired by the neural motor behaviors, a framework of broad learning based novel adaptive neural control is proposed in this article, such that in the presence of dynamic disturbance, robots can learn a set of basic skills and then generalize these skills to the neighboring movements naturally as our human motor system. This is achieved by incorporating the deterministic learning with the broad learning system that can accumulate and reuse the learned knowledge. The broad learning enabled adaptive neural control has been rigorously established in theory and tested in both simulation and experimental studies. Simulation results and performance of the Baxter robot in the experiments have shown the effectiveness and superiority of the proposed method in comparison to the conventional adaptive neural control.