A mathematical model for distribution network restoration after system blackout is developed. By changing the parameters of the goal function， the model can adapt to various cases of available power capacity in different restoration schemes. The genetic algorithm（GA） encodes with the ratio of branch and is decoded via the minimum spanning tree algorithm-Prim algorithm to bypass the generation of infeasible solutions， thus greatly improving the GA's efficiency. The backward/forward sweep algorithm is then adopted to solve the distribution power flow， and the sequence of nodes for power flow calculation is directly determined by the intermediate results of the Prim algorithm. Computational results on two test systems demonstrate the satisfactory performance of the robustness and convergence of the algorithm proposed.