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This paper describes a delayed predator-prey model with modified Leslie-Grower scheme, in which the time delays are regarded as bifurcation parameters. The functional response is considered to be of Holling-type II and incorporates a constant proportional prey refuge. The model is considered from the point of view of persistence and stability for this particular functional response. The asymptotic stability of coexist equilibrium is examined by using constructed Lyapunov function. The delayed system is analyzed with focusing on the gestation delay of predator τ . We investigate the occurrence of Hopf bifurcation in the neighborhood of the positive interior equilibrium. Moreover, the direction of the Hopf bifurcation and the stability of bifurcating periodic solution are analyzed. Finally, numerical simulations are carried out to verify the theoretical results of the paper. AMS Subject Classification: 92D25

ANALYSIS ON A MODIFIED LESLIE-GOWER AND HOLLING-TYPE II PREDATOR-PREY SYSTEM INCORPORATING A PREY REFUGE AND TIME DELAY