As the increasing penetration of wind and PV generations in island microgrids, the intermittent nature of renewable energy resources and randomness of load demands are inevitable, therefore, maintaining system stability and reliability has become a challenging issue for microgrid operators. In addition, energy storage unit and demand side management technology are widely utilized in the island micro grids to alleviate the passive impacts introduced by renewable energy resources. Nevertheless, they produce uncertainties as well. To accommodate the combined uncertainties, a two-stage robust model predictive control based optimization approach is proposed in this paper. The mixed integer quadratic programming model is established in the first operation stage to minimize the operation cost under the joint worst case of uncertainty, then an economic dispatch model is used to minimize the adjustment cost after obtaining actual data in the second operation stage. Robust linearization methods with the consideration of three types of uncertainty scenarios and uncertainty budgets are utilized in the first operation stage. Finally, the case study indicates that the proposed approach is more robust and economical than the conventional two-stage robust optimization approach, then the sensitivity of typical parameters and important units are analyzed and discussed. (C) 2018 Elsevier Ltd. All rights reserved.