A kind of fast multivariable generalized predictive control algorithm for Rössler hyperchaotic system is proposed. The chaotic system with improved recursive least squares parameter of time-varying forget factor is identified, then the output signals of the system follow fast the reference ones for the application of the feedforward gain matrix and softing coefficient matrix in regular performance index function of multivariable generalized predictive control. Moreover, the reduction of inverse matrix dimensions leads to smaller amount of computation of the algorithm. The simulation results show the effectiveness and practicability of this algorithm.