The design of distribution system is required to minimize the expectation of total responding time and expectation value of delivery cost under the time-based-competitive stochastic demands environment. Therefore, the multi-objective stochastic programming model for time-based-competitive distribution system with multi-source and multi-product was built when certain assumptions were given. Then, the stochastic model was tendered as the problem of certain type through the equivalent transform, and a heuristic algorithm was designed according to the specific structure of the model's decision space. A numerical calculation was performed in the model to solve an arithmetic problem in practical investigation. It showed that the decision model was practical and the algorithm was valid.