Considering the strength and deformation characteristics of concrete under different strain rates, a general strain rate independent elastoplastic damage model was first introduced based on the thermodynamics theory. Then, a strain rate dependent model was deduced by introducing strain rate sensitivity parameters in the general elastoplastic damage model. The numerical calibration of the modelling for concrete under different strain rates were performed. Study shows that this strain rate dependent model for concrete can well represent the main mechanical behavior and it is in good agreement with the experimental data. The proposed model can also be used to predict the failure stress in a large range of strain rates. Strain rate has a great influence on the mechanical properties of concrete materials.