Abstract: This Paper discusses a class of multivarable self-tuning controller with generalized cost-function. Relating to the demands of the engineering application with the cost-function, a generlized minimum-variance control strategy with prespecified closed-loop pole assignment is developed. Meanwhile the polynomial matrix R(Z^-1) in the cost-function is so determined as to elimineting the steady state output tracking error of the system. when the parameters of the system are unknown, the parameters of the controller may be estimated directly by using a muitivariable recursive least squares method. The convergent property of the proposed approach is given by using the Martingale convergence theory and the convergence conditions are also given .Simulation results show that the feasibility and the effectiveness of the proposed algorithm.