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The global stability on the dynamical behavior of the Leslie-Gower predator-prey system with delayed prey specific growth is analyzed by constructing the corresponding Lyapunov functional. Three different types of famous Holling's functional responses are considered in the present study. The sufficient conditions for the global stability analysis of the unique positive equilibrium point are derived accordingly. A numerical example is presented to illustrate the effect of different Holling-Type functional responses on the global stability of the Leislie-Gower predator-prey model.