In this paper, we study a stochastic predator-prey model with distributed delay and higher order perturbations. By the linear chain technique, we transform the stochastic system with weak kernel case into an equivalent degenerate system which contains three equations. By constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence of a stationary distribution of the positive solutions to the model. (C) 2019 Elsevier B.V. All rights reserved.