In this paper, the stability of an eco-epidemiological predator-prey model with saturation incidence. Using the theory of time-delay differential equations, the local stability of feasible equilibria is studied, and sufficient conditions for the occurrence of Hope branches at coexisting equilib are obtained. By constructing appropriate Lyapunov functional and applying the LaSalle invariance principle, the global asymptotic stability of feasible equilibria is discussed, and sufficient conditions are obtained for the elimination and spread of diseases to ultimately form endemic diseases.