High-quality β-Ga₂O₃ films were epitaxially grown by using metalorganic chemical vapor deposition (MOCVD) with different donor concentrations, and their shallow donor states were investigated by the temperature-dependent Hall measurement and secondary ion mass spectroscopy (SIMS) analysis. Two donor levels with ionization energies of ∼36 and ∼140 meV were extracted. It is found that the unintentional doping (UID) effects in MOCVD contribute substantially to both these two levels: the first donor level may come not only from silicon doping but also from unintentional substitution of carbon for Ga sites, and the second donor level probably comes from doubly charged defects related to unintentional H doping. By analyzing the relationship between the growth conditions and donor states, combined with density functional theory calculations, it is found that reducing the oxygen partial pressure during the growth might be a feasible way to reduce the UID effect. This work paves the way to the precise control of carrier density in Si-doped MOCVD β-Ga₂O₃ films.