We have developed a new nonstoichiometric Gd3+delta(Al,Ga)(5-delta)O-12:Ce garnet scintillator for an X-ray CT scanner. For commercially used scintillators, reproducible luminescence properties are of great importance. We have found that the afterglow properties of the garnet change drastically in the vicinity of the stoichiometric compositions. The most suitable properties are obtained at slightly excess (Gd,Ce) compositions from the stoichiometry. In order to investigate the afterglow properties, crystallography arrangements, phase equilibrium relationship between crystal phases, and luminescence characteristics of host material doped with different valence ions have been examined. The luminescence properties are explained by isoelectronic traps based on the difference in the electronegativity of the dopant and host ions, which would act as electron trap centers and hole trap centers within the band gap.