Using first-principles calculations, we investigate lithium vacancy and interstitial defects in lithium phosphate (γ-Li3PO4) and in its interface with metallic Li. We find that γ-Li3PO4 is good electronic insulator with a wide band gap of 6 eV. The calculated formation energies of Li vacancies are higher than those of Li interstitials, which indicate that the ionic conductivity is determined by the migration of Li interstitial defects in bulk electrolyte. The Li vacancy-interstitial pair defect formation energy in the Li/γ-Li3PO4 interface is comparable to the sum of Li vacancy defect at the electrode and Li ion interstitial defect in the electrolyte. Our calculation indicates that the low ionic conductivity of Li/electrolyte interface is associated with the high Li ion defect formation energy. Our study provides some useful insights on Li defect formation and migration mechanisms at the electrode-electrolyte interface and, hence, a research direction for designing future Li-ion batteries.