Dispersal-induced pattern formation is important from both fundamental and application points of view. Spatial pattern in an ecological system can strongly depend on exogenous factors like arrangement of the natural and artificial physical features of the habitat (topography) and distribution of resources. It is also influenced by endogenous factors (intrinsic biological forces) such as the ecological interactions of individuals. Here, we consider a discrete space–time host–parasitoid metapopulation model in the presence of both self-diffusion (due to endogenous factors) and cross-diffusion (due to exogenous factors). Dynamics of a metapopulation system consists of a dispersal stage and a reaction stage. In the dispersal stage, populations from an individual site can disperse to the nearest neighboring sites via dispersal and may cause variation in the host and parasitoid biomass of the node. In the reaction stage, hosts and parasitoids interact in each site and their local interaction is governed by the modified Nicholson–Bailey-type interaction. The conditions for the existence of pattern-forming instabilities (like Turing, Hopf and Hopf–Turing) in the reaction–diffusion discrete metapopulation model have been determined analytically, and the patterns have been visualized numerically. A wide range of complex spatiotemporal patterns (like periodic, quasi-periodic, chaotic) is observed with respect to the variation of diffusion coefficients and other local interacting parameters of the model. © 2020, Springer Nature B.V.