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This paper mainly studies a spatial predator–prey model with group defense and prey-taxis. The stability of the semi-trivial solution is examined by employing variational formulations and using the limiting behavior for the principal eigenvalue. Six different parametric restrictions dependent on the environmental carrying capacity are discussed to explore the effect of the prey-taxis and prey diffusion on the stability of the semi-trivial solution. Our analysis reveals that prey-taxis can change the stability of the semi-trivial solution in particular cases. Moreover, it is obtained that as long as the predator death rate is small enough, the predator can successfully invade no matter how the prey disperses. Numerical simulations illustrate that prey-taxis, group defense and environmental heterogeneity may have a synergistic effect on promoting predator invasion. It is determined that the intensity of environmental heterogeneity can affect the population size, and the predator may fail to invade due to the high environmental heterogeneity. Note that the role of group defense in predator invasion is related to the environmental carrying capacity. • Analyze predator invasion using principal eigenvalue variational formulations. • Prey-taxis can enable predators to successfully invade in heterogeneous environment. • The environmental heterogeneity can affect predator population evolution. • Group defense promotes predator invasion if carrying capacity is below the threshold. [ABSTRACT FROM AUTHOR]