The atomic and electronic structures are calculated for atomically uniform Ag layers on the Ga-induced Si(111)-(root 3 x root 3)R30 degrees surface by using the Density Functional Theory. It is found that when the amount of Ag atoms increases on the 1/3 monolayer Ga-induced Si(111)-(root 3 x root 3)R30 degrees surface, the equilibrium T-4 adsorption site of Ga atom changes to the T-1 site. We have determined a single covalent bond between Ga and Si atoms but there is some charge accumulation on the Ga-Ag layer, turning the surface to metallic nature. For 10 Ag monolayers, we have determined evolution of several quantum-well states within the energy range of 1 eV below the Fermi level. The energy separation between the quantum well states increases as their numbers develop below the Fermi level. The Ag film quantum-well states show in-plane parabolic dispersion, with splittings arising due to Umklapp features related to the Si(111)-(1 x 1) surface Brillouin zone. We have also identified Shockley type surface states, which show small Rashba-type spin-orbit splitting.