We present a first-principles calculation of the electronic structure near an antiphase boundary APB in magnetite, with the shift vector along the 110 direction and a 110 boundary plane. We have first used the local spin-density approximation to calculate the ground-state energy of a supercell with two magnetite grains separated by an APB, and found that this energy is lower when magnetite grains are coupled ferromagnetically. The LDA+ U approximation has later been used for an accurate description of the density of states near the boundary. Results show that localized electron states can exist in the vicinity of the structural defect. We give a clear description of the dispersion of these APB states.