Abstract: A predator-prey system of two species with stage structure and time delay is considered.The invariance of non-negativity,nature of the boundary equilibria,permanence and global stability are analyzed.The results show that positive equilibrium is locally asymptotically stable when time delay τ is suitable small,while a loss of stability by a Hopf bifurcation can occur as the delay increase.That is,a family of periodic solutions bifurcates from positive equilibrium as τ passes through the critical value τ0.