In this paper, the Johnson-Holmquist concrete (JHC) constitutive model is adopted for modeling and simulating the fracture of dolomite. A detailed step-by-step procedure for determining all required parameters, based on a series of experiments under quasi-static and dynamic regimes, is proposed. Strain rate coefficients, failure surfaces, equations of state and damage/failure constants are acquired based on the experimental data and finite element analyses. The JHC model with the obtained parameters for dolomite is subsequently validated using quasi-static uniaxial and triaxial compression tests as well as dynamic split Hopkinson pressure bar (SHPB) tests. The influence of mesh size is also analyzed. It shows that the simulated fracture behavior and waveform data are in good agreement with the experimental data for all tests under both quasi-static and dynamic loading conditions. Future studies will implement the validated JHC model in small- and large-scale blasting simulations.