To facilitate the pre-estimation and optimization of the prescription design of a multi-component polymer bonded explosive (PBX), a multicomponent mesoscopic reaction rate model (MC-DZK model) is developed to predicate preferably the influence of both the explosive components and the particle size of on the shock initiation. All the parameters in the model are determined directly by the parameters in the DZK model for each explosive component. Furthermore, for the multicomponent insensitive explosive PBXC10 (70% TATB, 25% HMX, and 5% Kel-F800 by weight) with different explosive particle sizes, both shock initiation experiments and corresponding numerical simulations are performed, and there is satisfactory agreement between the numerical results and the available experimental data. It is found that the pressure histories present as a shape of step increase during the whole shock initiation process, which is resulted mainly from the rapid chemical reaction rate just behind the precursory shock wave front. It is also found that the smaller the size of the explosive particulates, the faster the pressure grows on the precursory shock wave front, the shorter the run distance to detonation, and the higher the chemical reaction rate just behind the precursory shock wave front.