A new mesoscale numerical model is presented adopting finite element method to simulate the dynamic properties of concrete. A new constitutive law based on Kelvin viscoelastic model is utilized to characterize the evolutionary processes of damage under dynamic load. The finite element method is utilized for discretization of components of concrete block, which are aggregate, cement and interfacial transition zone between the aggregate and the mortar. The strengths of these components and viscous parameters are adopted according to Weibull distribution. The dynamic analysis of concrete block is performed by using this model and the calculated result is discussed. The result shows the proposed model can characterize the dynamic properties of concrete well.