In this paper, we consider the dynamics of stochastic predator–prey models with Holling II functional response. For the stochastic systems, we firstly establish sufficient conditions for the existence of the globally positive solutions. Then we investigate the asymptotic moment estimations of the positive solutions and study the ultimately bounded in the mean of them. Thirdly, by constructing some suitable Lyapunov functions, we verify that there are unique stationary distributions and they are ergodic. The obtained results show that the systems still retain some stability in the sense of weak stability provided that the intensity of the white noise is relatively small. Finally, some numerical simulations are introduced to illustrate our main results.