A kind of fast generalized predictive function control algorithm with convergence of tracking for Hnon chaotic system is proposed. First, based on the existing generalized predictive function control algorithm, the matrix inversion computation in the control law is avoided because special basis functions are selected according to the motion characteristics of chaotic system and the change trend of practical control input. Then, by introducing the determinate feedforward gain matrix into performance index function, it is convergent that the output of Hnon chaotic system follows reference signal. The simulated results show the effectiveness of this algorithm.