Dynamic compressive tests of plain concrete specimens (C30 and C40) are carried out on MTS, with the uniaxial strain rate ranging from 10-5/s to 10-2/s. The impacts of strain rates on concrete strength are studied systematically. The mechanical properties of compressive strength, elastic modulus and compressive stress-strain curve of concrete under different stain rates are also analyzed. The experiental relationships between strain rate and compressive strength of concrete are established. It is found that the compressive strength of concrete increases with the strain rate increasing. Modulus is also showing a growth trend, but the growth rate varies greatly; and the stress-strain curve under dynamic loads is similar to the one under static loads. These research achievements can provide us with a more accurate grasp of concrete actual working conditions and provide some guidance to structural design of concrete. These are important to build the dynamic damage constitutive models, too.