Despite its ubiquitous presence in the built environment, the dynamic tensile fracture behaviour of concrete under a high strain rate is still not completely understood. In this study, a three-dimensional meso-scale finite element model is developed to investigate the dynamic tensile fracture behaviour of concrete. On the meso-scale, concrete is regarded as a composite of aggregate, mortar and the interface transition zone (ITZ). The nucleation, coalescence, and propagation of cracks are modelled by pre-insert rate-dependent cohesive elements. Predicted results of the proposed numerical model fit well with experimental data in spall tests. The evolution of cracks in concrete under dynamic loading is explicitly presented. The micro-cracks of concrete are widely distributed before the initiation of macro-cracks. The results suggest that the inertia effect plays an important role in the dynamic fracture behaviour of concrete. Moreover, the influence of the mesostructure on the dynamic tensile strength is investigated. The dissipated fracture energy under dynamic loading is also indicated to be affected by the mesostructure of concrete.