Through first-principles calculation using the screened hybrid functional, we investigate the energetics and electronic structure of substitutional hydrogen (HO) in which one hydrogen replaces an oxygen atom in LaAlO3. The calculated binding energy between the hydrogen and the oxygen vacancy (VO) indicates that HO is energetically likely to form in the oxide. HO releases one electron to the conduction band, so it is a shallow donor. Most importantly, HO completely eliminates the in-gap defect states associated with VO, suggesting that hydrogen can be used as passivating agent for VO acting as a carrier trap or fixed charge in the oxide and near the oxide/semiconductor interface in LaAlO3-based devices.