This paper,using Hammerstein model to express a kind of nonlinear system,presents a new kind of Adaptive Generalized Predictive control for Nonlinear systems(NAGPC). This method divides the whole system into two parts: linear subsystem and nonlinear one. In the first part,a new algorithm ,whose computation quantity is less and speed is faster,is developed according to the characteristics of gain controlling Matrix F in the Generalized Predictive Control (GPC). Mean while, the interpolation method is used to develop one step root solving procedure and the result can be used as the whole system input in the second part. Simulation studies show that the general algorithm NAGPC is strong in robustness,good in stability and fast in computation.