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This paper is concerned with a nonlocal reaction–diffusion prey–predator model with free boundary. The spatial–temporal risk index R 0 p (t) which is threshold value, is introduced for this model. The global existence of positive solutions is proved and the long-time behavior of positive solutions is investigated. The sufficient conditions are found for vanishing of predators and the establishment of themselves in new environment. Furthermore, the spreading–vanishing criteria are established. The results show that the predators will vanish finally and not establish themselves if the sizes of habitant and spreading coefficient are relatively small or the initial value of predators is also relatively small with R 0 p (0) < 1 , and the predators will achieve if initial values of predators and preys are relatively big or R 0 p (t 0) > 1 for t 0 > 0. [ABSTRACT FROM AUTHOR]