In this article,we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlinear incidence rates and distributed delays.By using strict monotonicity of the incidence function and constructing a Lyapunov functional,we obtain sufficient conditions under which the endemic equilibrium is globally asymptotically stable.When the nonlinear incidence rate is a saturated incidence rate,our result provides a new global stability condition for a small rate of immunity loss.