This paper focuses on a SIRS infectious model of nonlocal dispersal adopted with age structure. We primarily investigate the existence and nonexistence of traveling wave solutions connecting the disease-free equilibrium state and the endemic equilibrium state. To be more precise, we obtain the existence of traveling wave solutions by constructing suitable upper and lower solutions and then applying Schauder's fixed point theorem when $R_0>1$ and $c>c^{\ast }$. In addition, we prove the nonexistence of traveling wave solutions by applying the Laplace transform for $R_0>1$ and $0<c<c^{\ast }$.