<p>In this paper, a novel three-species two patch prey-predator model is considered in both theoretical and numerical ways, which incorporates prey refuge and constant time delay. Firstly, for non-delayed model, based on the work of Dubey in 2007, we extend some of the results by relaxing the restrictions on the parameters and give some additional explanations. By Lyapunov’s second method, for any choices of parameters, we proved that all solutions converge to a globally asymptotically stable positive equilibrium. Furthermore, we incorporated a discrete delay into the model, the time delay refers to the period from the capture of the prey in the unreserved area by the predator to its conversion to predator biomass, and proved all solutions of the system are nonnegative and eventually bounded. For the delayed model, by the criterion of Beretta and Kuang, we give out the existence and stability theorem of Hopf bifurcation. Finally, the abundance of steady state chaotic solutions is identified through computer simulations that utilize the numerical continuation software XPPAUT and DDE-BIFTOOL. In detail, as the increasing of the delay, the predator will die out. Before extinction of the predator, when we choose the delay as the bifurcation parameter, rich dynamical behaviors including Hopf bifurcation, period doubling bifurcation and strange attractor have been exhibited, the chaotic solutions appear via a cascade of period-doubling bifurcations. The positive equilibrium experiences transcritical bifurcation at the critical value corresponding to die-out. Thus, the analysis and observations presented in this paper are of interest in the research fields of mathematics and biology.</p>