Abstract: A system of retarded functional differential equations is proposed as a predator-prey model with time delay in two-patches. The invariance of non-negativity,nature of boundary equilibria and global stability are analyzed.We show that positive equilibrium is locally asymptotically stable when time dalays τ=τ_1+τ_2 is suitable small, while a loss of stability by a Hopf bifurcation can occur as the delays increase.