Two luminescence bands from zinc oxide (ZnO) nanoparticles have been known and experimentally observed previously. The unanswered question is the mechanism leading to the visible spectrum in the blue or green region. So far there have been many postulations trying to elucidate this phenomenon, but none of them gives a mathematical expression that simultaneously expresses these two spectra. Here we interpret this phenomenon as the combination of distribution functions and the density of states of electrons and holes, precisely the product of the both. From the analysis, the narrow UV emission is predominantly attributed to the quantum confinement, and the product of the density of states and the distribution functions determines the visible spectrum. We find that varying the density and the effective mass of holes causes pronounced effect on both UV and visible, which reflects the fact of acceptors taking the main responsibility in the experimental observations.