For the nonlinear nature of the speed-regulating system of the induction motor and inverter, a control strategy based on the Hammerstein model and the neural network(NN) is proposed. The Hammerstein model is used to model the speed-regulation system of the induction motor and inverter. The model can be divided into two parts: the static nonlinear module and the dynamic linear module. Firstly, the auto-regressive and moving average(ARMA) model is used to identify the dynamic linear module of the speed-regulating system, and it is used as a reference model for identifying the inverse model of static nonlinear module in the framework of the model reference adaptive control method. The inverse model is modeled based on the NN and cascaded with the speed-regulating system to realize the NN direct inverse control strategy. Considering the existing of load disturbance, the on-line learning neural network direct inverse controller is also studied. Simulation results show that the proposed control strategy has high performance.