The geometrical structure of Y3Al5O12 (YAG) crystal was optimized by using first-principles calculation scheme, i.e. generalized gradient approximation (GGA) with the PW91 exchange correlation potential and “on the fly” pseudo-potential (OTFPP). The obtained lattice parameters are in good accordance with experimental results reported in the literature. This confirms the validity of the present GGA-OTFPP scheme. The total energy, populations, and contour maps of total charge density of YAG system were calculated with the same scheme. The derived formation energy (-2.396eV) indicate the good stability of the structure. The obtained Mulliken charge populations of atoms, overlap populations, as well as contour maps of total charge density congruously show that YAG crystal is a mixed bond material with stronger ion bond and weaker covalence bond.