We study the problem of minimum-variance control of linear time-varying discrete-time systems. We consider the standard time-varying controlled autoregressive moving-average model and develop a time-varying controller that guarantees both closed-loop stability and minimum-variance output control for a large class of linear time-varying systems. The controller is based on our previous results on minimum-variance prediction for linear time varying systems. We also show that the standard minimum-variance controller cannot in general guarantee closed-loop stability when applied to linear time-varying systems. However, a simple modification can make the closed loop stable.