We investigate the microscopic structures of interstitial and substitutional hydrogen impurities in LiNbO3 through the first-principles pseudopotential total-energy calculations. The interstitial hydrogen is located between two O atoms and bonds to one of the oxygen atoms. The hydrogen impurity substituting Li is significantly displaced from the Li-site and strongly bonds to an oxygen atom and is located on a biaxial axis of an O triangle. We discuss the effect of hydrogen to the ferroelectric polarization and the energetics for the trap of the interstitial hydrogen at a Li vacancy. (C) 2001 American Institute of Physics.