In order to optimize the distributed generation(DG) installation position and capacity, a multi-objective model of DG optimal allocation is established, in which the total deviation of node voltage, the investment of DG and the cost of operation and maintenance, the cost of network loss as well as the cost of purchasing power is taken as the objectives. The probabilistic model of DG and the load is sampled by Latin hypercube sampling for the purpose of taking into account the uncertainties of the distributed generation power output and the load. The multi-objective model is solved to obtain a Pareto solution set by non-dominated sorting genetic algorithm-II (NSGA-II). On the basis of information entropy weight, an algorithm of multi-objective grey target decision making with information entropy weight is applied to choose the optimal solution from the Pareto solution set. The simulation is conducted on a 25-node distribution system. The results verify the feasibility and effectiveness of the proposed method.