For a standard autoregressive moving average system with extraneous input this paper designs a weighted adaptive minimum variance controller based on a weighted least-squares algorithm. It is shown that the closed-loop system is stable, the general adaptive tracking is asymptotically optimal and the closed-loop transfer function is invariant, with its denominator differing from a fixed value. It is found that there is an equivalent relation between the consistent estimation and the system stability. Simulation demonstrates that the results developed in the paper are efficient. No a priori information for the unknown input coefficient and no modification for its estimate are made.