An aluminized melt-cast Duan–Zhang–Kim mesoscopic reaction rate model based on the pore collapse hot-spot ignition mechanism is proposed to characterize the shock initiation behavior as well as size effects of explosive particles on the shock initiation of aluminized melt-cast explosives. For aluminized 2,4-dinitroanisole (DNAN)-based melt-cast R1 explosives [containing 60 wt. % HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazoncine), 30 wt. % DNAN, and 10 wt. % aluminium] with different particle sizes of HMX, both shock initiation experiments and corresponding numerical simulations were performed. The numerical results are found to be in good agreement with the experimental data, by which the mesoscopic reaction rate model is verified and the model parameters for the R1 explosive are determined. It is also found that the smaller the particle size of the granular explosive component, the faster the leading shock wave propagates, and the faster the detonation growth inside the aluminized melt-cast explosive.