As the dynamic behavior of the concrete is different from that under static load, this research focuses on the study of dynamic responses of concrete by simulating the split Hopkinson pressure bar (SHPB) test. Finite element code LS-DYNA is used for modeling the dynamic behaviors of concrete. Three continuous models are reviewed and the Holmquist-Johnson-Cook model (HJC) is introduced in detail. The HJC model which has been implemented in LS-DYNA is used to represent the concrete properties. The SHPB test model is established and a few stress waves are applied to the incident bar to simulate the dynamic concrete behaviors. The stress-strain curves are obtained. The stress distributions are analyzed. The crack initiation and propagation process are described. It is concluded that: the HJC model can modeling the entire process of the fracture initiation and fragmentation; the compressive of the concrete is significantly influenced by the strain rates.