The chemical evolution of the Galaxy with a pulsating active nucleus is investigated. The surface densities of gas, stellar remnants, stars and chemical species such as helium and heavy elements inZ≧6 are calculated as functions of the position in the Galaxy and of the evolutional time of the Galaxy. According to this model, the entire luminosity of the galactic disk becomes almost constant at some 2×109 yr after the galactic formation, but the nuclear bulge, whose dimensions gradually diminishes, becomes more and more luminous with time. On the other hand, the abundance depletion of helium and heavy elements appears in the inner region of the disk after some 6×109 yr of the galactic formation. It also becomes clear that the activity for the nucleosynthesis in the nucleus is limited only in the early history of the Galaxy and has been reduced rapidly with time. Using this model, we can account for the observed phenomena such as the smooth dependence of the elemental abundance in the halo population on the distance from the galactic center, the high abundance of heavy elements in quasar spectra and etc.