The intermittent of DG makes it difficult to predict power output, consequently the optimized result will be inaccurate. This paper proposes a probabilistic generation-load model to convert the problem of random output into an issue of certainty. Meanwhile, considering the effect of DG on distribution network, this paper establishes a multi-objective model, which considers the construction and operation fees, network loss, reliability and environmental factor. A quantum differential evolution optimization (QDE) algorithm is put forward to determine the optimal site and capacity of DG in the network. The algorithm takes advantage of its probability expression and superposition state, which potentially improves the searching ability. Besides, crossing and variation operation of QDE helps maintain population diversity. The analysis of results proves reasonableness and feasibility of the proposed model and algorithm.