Uncertainty set is used to describe the uncertain fluctuation characteristics of distributed wind power and photovoltaic (PV) output in microgrid, and the minimum total operation cost of microgrid in the extreme scenario is taken as the objective function, the robust optimization scheduling model of island microgrid is established. In the model, frequency characteristics of diesel generators, energy storage devices, lines and loads in microgrid are considered. The Benders decomposition algorithm is used to solve the robust optimization scheduling model, by decomposing the original problem into a main problem and a sub problem and using alternating iteration to solve these two problems, the scheduling scheme of minimizing the total operation cost in the extreme scenario with the highest network loss is obtained. Test results on an island microgrid show that the obtained optimal scheduling scheme can effectively deal with the uncertain fluctuation of wind power and PV output, ensure that the system frequency will not exceed the security limit, and has the characteristics of robustness.