The analogy of traffic flow to water flow has been well known. But some essential differences exist, e.g. anisotropy, viscosity, and the extent to which conservation law holds. Not surprisingly, this is due to different manners in which water particles and vehicles move and interact. In this study, we investigate and model the viscous behavior exhibited by traffic flow. We attribute the viscous effect of traffic flow to drivers’ heterogeneity in terms of their preferred driving speeds. A model incorporating the diffusion effect is developed based on the idea of characteristic curve. In particular, the governing equation of the traveling platoon is explicitly derived from this model. In accordance with our postulation, the derived equation includes one viscosity term. The proposed model is best suited for the analysis of the local fine structure of traffic flow which is conventionally represented as a shock.