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Abstract The dynamics of a diffusive predator-prey system with prey refuge and gestation delay is investigated in this paper. For a non-delay system, global stability, Turing instability and Hopf bifurcation are studied. For a delay system, time delay induced instability and Hopf bifurcation are discussed. By the theory of normal form and the center manifold method, the direction and stability of the bifurcating periodic solution are discussed.