Hexagonal α-Fe2O3 is one of the most common functional material used as magnetic semiconductor, and plays an important part in various applications, such as electronic devices etc. Based on the density functional theory, the lattice parameters, density of states and Bader charge analysis of α-Fe2O3 have been calculated using the first-principles calculation with GGA+U method. As Fe is a transition metal element, the value of U can be more accurate by considering the influence of the strong on-site Coulomb interaction between 3d electrons. First, the crystal equilibrium volume, the magnetic moment of Fe atom, and the band gap value of α-Fe2O3 are synthetically researched and compared with those with different U. Results indicate that the calculation model of α-Fe2O3 are in good agreement with the experimental model when the value of U is 6 eV. These parameters can also be adapted to the following doping calculaton. The α-Fe2O3 unit cell has both tetrahedral and octahedral interstitial sites. The calculation of doping formation energy shows that the α-Fe2O3 system is most stable when the doped hydrogen atom is in the tetrahedral interstitial site. The density of states show that the valence band and conduction band compositions are similar for the bulk and hydrogen-doped α-Fe2O3. That is, the valence bands are dominated mainly by both O 2p and Fe 3d orbitals with the O 2p orbitals playing a leading role, while the conduction band is dominated by Fe 3d orbitals. The band gap of α-Fe2O3 decreases from 2.2 to 1.63 eV after hydrogen doping. Also, a strong hybrid peak occurs near the Fermi level after hydrogen doping, which is chiefly composed of Fe 3d orbital, and the O 2p orbital also has a small contribution. The H 1s orbital is mainly in the lower level below the top valence band. Results of the Bader charge analysis and the density of states calculation for partial correlated atoms suggest that the new hybrid peak is chiefly caused by Fe atom which is closest to the hydrogen atom in the crystal cell. In this process, H atom loses electrons, and the nearest neighbors of H atom, i.e. O and Fe atoms, almost obtain all the electrons H atom loses, so H and O atoms are bonded together strongly, causing the hybrid peak, to expand the width of the top valence band and shift down the bottom of the conduction band, so that the band gap decreases and the electrical conductivity increases. Hydrogen doping is suggested to be an effective method to modify the band.