Abstract： A stage-structured predator-prey system of population growth con-sisting of immature and mature individuals is proposed with a mature population ofharvesting, the growth of predator population is of Holling Ⅱ type with time delay andratio-dependent(which can be roughly stated as that the per capita predator growthrate should be a function of the ratio of prey to predator abundance). We establishconditions under which positive equilibrium of the system is locally and globally asymp-totically stable and the optimal harvesting of the mature population is also considered.