The formation and mobility of Li point defects in Li2B4O7 are investigated theoretically with periodic quantum chemical calculations. Calculated defect formation energies obtained with a density functional theory/Hartree-Fock hybrid method and with the Perdew-Wang density functional method are compared. The basis set effect is investigated by comparison of results obtained with atom-centered basis functions and plane waves. With both methods only a moderate relaxation is observed for the atoms surrounding the Li defect position. The defect-induced change of electronic properties is investigated by calculating the density of states for the stoichiometric and defective supercells. The activation energy for the movement of a Li+ ion along the ( 001) direction is calculated. It is observed that Li+ ion migrates through a one-dimensional channel formed by the five-vertex lithium-oxygen (LiO5) polyhedra. The calculated activation energies are in excellent accord with experiment.