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• Effect of spatial average and delay on the predator-prey model is investigated. • Conditions for stability, steady state bifurcation and Hopf bifurcation are obtained. • Algorithm of normal form of steady state-Hopf bifurcation for system with spatial average and delay is derived. • Spatiotemporal dynamical classification near the steady state-Hopf bifurcation point is studied. In this paper, we discuss a diffusive predator-prey model with nonlocality and delay. Stability and bifurcation analysis suggest that the joint impacts of the nonlocal term and delay result in instability of the positive constant steady state. Moreover, steady state, Hopf and steady state-Hopf bifurcations and interactions of these bifurcations may occur under certain conditions. Normal forms of steady state, Hopf and steady state-Hopf bifurcations for a general reaction-diffusion model with nonlocal effects and delay are derived. In numerical simulations, spatially inhomogeneous steady states and periodic solutions and heteroclinic connections between these solutions are obtained. [ABSTRACT FROM AUTHOR]