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To avoid the shortcoming of the traditional (previous)generalized predictive control (GPC) algorithms, too large amounts of computation, a fast algorithm of multivariable generalized predictive control is presented in which only the current control actions are computed exactly on line and the rest (the future control actions) are approximately done off line. The algorithm is simple and can be used in the arbitary-dimension input arbitary-dimension output (ADIADO) linear systems. Because it dose not need solving Diophantine equation and reduces the dimension of the inverse matrix, it decreases largely the computational burden. Finally, simulation results show that the presented algorithm is effective and practicable.