Abstract: The static size effect of concretes has been relatively well addressed, while studies on the dynamic size effect of concretes have not yet generated a unified understanding. The size effect of concrete can be attributed to the inner heterogeneities. Herein the study, a meso-scale simulation method was built to study the dynamic failure and size effect of concrete. Considering the material heterogeneity and strain rate effects of meso-components, concrete was simulated as a three-phase composite composed of aggregate, mortar matrix and interface transition zone at meso-scale. The square concrete specimens with different sizes were built and the dynamic compressive failure and the size effect of concrete under the strain rates from 10^-5 s^-1 to 200 s^-1 were investigated using the meso-scale simulation method. There are obvious differences between static size effect and dynamic size effect in the compressive strength of concrete. There exists a critical strain rate (the critical strain rate is s^-1 approximately). When the applied strain rate is less than the critical strain rate, the size effect on the dynamic compressive strength is weakened or suppressed as the strain rate increases. The dynamic compressive strength would be independent of the structural size of the specimen when the applied strain rate reaches the critical strain rate. When the applied strain rate is more than the critical strain rate, the size effect on the dynamic compressive strength is strengthened as the strain rate increases. Finally, based on the simulation results, the mechanism of concrete dynamic size effect was analyzed and discussed.