A kind of generalized predictive control fast algorithm with predictive function for Hénon chaotic system is proposed. Firstly, we identify the chaotic system by recursive least square parameter of time varying forget factor. Then one kind of predictive function is added into this algorithm and makes full use of compensation of predictive information, overcoming the disadvantage of calculating inverse matrix to increase the response speed of the system. The ability of tracking the reference signal and restraining the parameter perturbation and stochastic disturbance are improved. Simulated results show the effectiveness of the algorithm.