In this paper, we have proposed a reaction-diffusion SIRS epidemic model with a general incidence function f ( S , I ) in a spatially heterogeneous environment. For this model, we derive the basic reproduction number R 0 and establish the results of the threshold dynamics with respect to the basic reproduction number R 0 . Specifically, the disease-free equilibrium is globally asymptotically stable when R 0 < 1 , while the disease persists if 1 $ ]]> R 0 > 1 . Especially, under the spatially homogeneous condition, the SIRS model admits a unique steady state, which is globally asymptotically stable under some assumptions when 1 $ ]]> R 0 > 1 . Finally, we take the Beddington-DeAngelis-type incidence function and perform some numerical simulations to illustrate the dynamics of the solutions as the model parameters are varied.