The desensitization characteristics of explosives significantly affect the shock initiation process of explosives, making it difficult to determine the initiation conditions of explosives. A one-dimensional Lagrange fluid dynamics code was developed based on the Arrhenius shock temperature state dependent Wescott–Stewart–Davis (AWSD) reactive burn model to investigate the response characteristics of 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) based heterogeneous explosive TATB-2 under double-shock wave. The parameters of the equation of state and the reactive burn model were calibrated based on the experimental data of one-dimensional sustained pulse for TATB-2 explosive. The shock initiation process of TATB-2 explosive under double-shock wave was simulated and compared with the experiments. The results show that the AWSD model can well reproduce the shock initiation process of TATB-2 explosive under double-shock wave. In addition, the desensitization characteristics of TATB-2 explosive under double-shock wave were revealed by analyzing the distance to detonation, reaction degree, and temperature rise.