The microgrid is considered to have promising development and practical application due to its characteristics of efficiency, economy and promoting the accommodation for renewable distributed generation (RDG). However, the uncertainties originated from the RDG pose challenges to the reliable operation and real-time management of microgrid. To cope with this problem, this paper proposes a real-time economic dispatch strategy of the microgrid by combining the model predictive control (MPC) and robust optimization (RO). The proposed robust MPC based strategy formulates the MPC optimization as a robust problem, which enables the real-time energy dispatch of the microgrid while ensuring its reliable operation. Meanwhile, the feedback update mechanism of MPC contributes to reduce the conservativeness of RO. In addition, the proposed solution considers the demand response (DR) of electricity load to further reduce operating cost. The effectiveness of the proposed solution is demonstrated by simulation experiments and comparison with the benchmark.