Considering the impact of distributed energy generation and load uncertainty in microgrid, a random framework based on cloud theory is put forward, and change the fuzziness and randomness of uncertainty in microgrid into a quantitative form by using cloud model. Then establish the reconstruction model of microgrid by using the optimization objectives of network loss minimize and power quality optimize, besides, a fuzzy comprehensive evaluation method based on fuzzy mathematics is used to deal with the multi-objective function, and propose a correctional Big Bang-Big Crunch algorithm to solve the model. At last, a case study is carry out with the standard model of 33-bus microgrid, the simulation results show that the proposed model and algorithm are effective and practical.