Using hybrid density functional theory, we investigated formation energies and transition energies of possible donor-like defects in GaInO3, with the aim of exploring the sources of the experimentally observed n-type conductivity in this material. We predicted that O vacancies are deep donors; interstitial Ga and In are shallow donors but with rather high formation energies (>2.5 eV). Thus these intrinsic defects cannot cause high levels of n-type conductivity. However, ubiquitous H impurities existing in samples can act as shallow donors. As for extrinsic dopants, substitutional Sn and Ge are shown to act as effective donor dopants and can give rise to highly n-type conductive GaInO3; while substitutional N behaviors as a compensating center. Our results provide a consistent explanation of experimental observations.