This work aims to study a population-dispersal dynamics for predator–prey interactions in a two patch environment with strong Allee effect among prey species in both patches. It is assumed that the prey species are movable and their dispersal between patches is directed from lower fitness to the higher fitness patch (exhibiting balanced dispersal). Existence and stability criterion of the interior equilibrium point of the system is analyzed in presence as well as in absence of dispersal speed. It has been observed that Allee threshold takes an important role to destabilize the system while the prey individuals evolve in their own patches independently. Moreover dispersal cannot destabilize populations at the interior equilibrium, i.e., if a predator–prey equilibrium without dispersal is in stable state then this situation cannot be destabilized when prey species move between two patches. Numerical simulations using MATLAB validate the analytical results. The occurrence of transcritical as well as Hopf bifurcation has also been reported.