Summary: This paper proposes a general method based on a property of zero-sum two-player games to derive robust optimal monetary policy rules – the best rules among those that yield an acceptable performance in a specified range of models – when the true model is unknown and model uncertainty is viewed as uncertainty about parameters of the structural model. The method is applied to characterize robust optimal Taylor rules in a simple forward-looking macroeconomic model that can be derived from first principles. Although it is commonly believed that monetary policy should be less responsive when there is parameter uncertainty, we show that robust optimal Taylor rules prescribe in general a stronger response of the interest rate to fluctuations in inflation and the output gap than is the case in the absence of uncertainty. Thus model uncertainty does not necessarily justify a relatively small response of actual monetary policy.