Based on the statistical damage theory， a statistical damage constitutive model of the concrete under uniaxial compression is established with considering the strain rate effect. Two meso-damage modes of fracture and yield are considered. The critical state is regarded as the transition point from uniform damage stage to local failure stage， which lags behind the peak stress state.Under dynamic loading， the mechanical performance in meso-structure of the concrete is changed， and the growth form， path and number of the microcracks are also significantly changed compared to the quasi-static state. As a result， the meso-damage evolution process is changed， which could be characterized by five characteristic parameters. The uniaxial dynamic compression test is conducted， and the stress-strain curves within the limits of 10?5/s~10?2/s are obtained. The rationality of the model is verified by six groups of experimental data. It shows that the prediction curves are in good agreement with the test curves， and the characteristic parameters show obvious regularity with the strain rate. The model can well describe the dynamic mechanical behavior of the concrete， and establish an effective connection among the strain rate effect mechanism， the meso-damage mechanism， and the macrononlinear behavior.