In this paper, a stochastic competitive model with distributed time delays and Lévy jumps is formulated. With or without a polluted environment, the model is denoted by (M) or (M0), respectively. The existence of positive solution, persistence in mean, and extinction of species for (M) and (M0) are both studied. The sufficient criteria of stability in distribution for model (M) is obtained. Finally, some numerical simulations are given to illustrate our theoretical results.