Concrete as a main structural material has been widely used all over the world. It is of interest for researchers to understand the damage process of concrete material under blast loading. Concrete is a composite material, consisting of aggregate bounded by cement paste, which makes the material behaviour of concrete very complicated. The distribution of coarse aggregates affects the crack pattern and the fragment size distribution when it is under blast loads. But most of the present dynamic concrete material models are based on homogeneous material assumption, which often makes the prediction of fragment size distribution and crack propagation of concrete material under blast loads unreliable. In this study, a mesoscale heterogeneous model for concrete material is developed. In the mesoscale model, the concrete is assumed to consist of two phases, that is, coarse aggregates and mortar matrix with fine aggregate dissolved in it. The high strength coarse aggregate is assumed to be circular with a randomly distributed radius. The aggregate particle size distribution is based on one of the most popular aggregate distributions, i.e., Fuller's curve. The spatial distribution of coarse aggregate is also assumed to be random in the structure components. With the suggested distribution a dynamic damage model for concrete is developed. The material model is incorporated in the hydrocode AUTODYN. As a numerical example, the dynamic damage process of a concrete slab under blast loads is analyzed. Taguchi method is adopted to analyse the effect of some crucial parameters.