In this paper, we focus on a production-distribution system consists of a producer and a distribution center. We formulate a bilevel multiobjective programming model for it. The upper model is to maximize the producer’s profit and the lower model is to maximize both the distribution center’s profit and customers’ satisfaction degree. Some decision parameters, including unit production cost, customers’ demand and unit sale price, are assumed as fuzzy random variables due to complex decision environment. Chance-constrained technique are used to tackle the uncertainty of this model. A modified genetic algorithm is be used to solve the problem. A numerical example illustrates the effectiveness and efficiency of the model and the algorithm.