A series of shock initiation experiments on the explosive PBXC03 (87 % HMX, 7 % TATB, and 6 % Viton by weight) with different particle sizes and porosities under various shock loadings have been performed, and it is found that the particle size and the porosity of the explosives have much influence on the shock initiation characteristics. That is, the smaller the particle size, the more difficult the explosive to be ignited but the faster the detonation grows once the explosive is ignited. It is also found that the detonation grows the fastest in the explosive with moderate porosity. Moreover, a modified mesoscopic reaction rate model based on the experimental results and the pore collapse hot-spot ignition mechanism is developed, which allows for a separate reaction mechanism evaluation at different reaction stages for the shock initiation and detonation growth processes in the explosives. The calculated pressure-time histories and Pop-Plots for PBXC03 are founded to be all in good agreement with the experimental data. The modified mesoscopic reaction rate model shows its potentiality for quantitatively predicting the effects of the mesostructure of PBXs on the shock initiation and detonation growth processes with a high degree of confidence.