We develop a numerical scheme to investigate the high-order harmonic generation (HHG) in intense laser-matter interactions. Tracing the time evolution of every electronic laser-field-free state, we observe the HHG in a time-integrated quantum transition picture. Our full-quantum simulations reveal that continuum electrons with a broad energy distribution contribute equally to one harmonic and the excited state also plays an important role in the molecular HHG. These results imply a laser-intensity-dependent picture of intramolecular interference in the HHG.