In this research article, we considered an ecological prey predator fishery model system with a generalized case where both the patches are accessible to both prey and predator. We suppose that the prey migrate between two patches randomly. The growth of prey in each patch in the absence of predators is assumed to be logistic. The predator consumes the prey with intrinsic growth rates in both the patches. The existence of its steady states and their stability (local and global) are analyzed. It is also emphasized the diffusive stability of the system along with some numerical simulations. Numerical simulation has also been performed in support of analysis by using MATLAB. © 2006-2017 Asian Research Publishing Network (ARPN).