The purpose of this paper is to study the existence and non-existence of traveling wave solutions for a diffusive age-structured SIR epidemic model. One of the main features of this model is that the susceptible, infected and removed individuals are all involved in this model, and the total population is not assumed a constant. In this paper, we show that the basic reproduction number R 0 corresponding to the spatially homogeneous system is an important threshold parameter in determining the existence of the traveling wave solutions. More precisely, when R 0> 1 and the wave speed is greater than the minimal wave speed c*, we establish the existence of traveling wave solutions. On the other hand, when R 0> 1 and 0< c< c* or R 0< 1, we show the non-existence of traveling wave solutions. Our study provides some insights on how to deal with the high dimensional age-structured epidemic models.