A generalized minimum variance controller is developed for linear time-varying systems. The plants to be controlled are described using a controlled auto-regressive moving average model and are exponentially stable. Both, the plant parameters and the noise variance are time-varying. The generalized minimum variance cost functional is the sum of a tracking error variance between a filtered plant output and a filtered reference plus a penalty term of filtered plant input. Time-varying filters are introduced for weighting to make the controller more flexible.