The paramagnetic electronic structure calculations of the R 3 Al 5 O 12 (R ¼ Ce2Lu, the rare-earth elements) systems by substituting Y atoms in Y 3 Al 5 O 12 ðYAGÞ with R atoms, using the tight-binding linearized muffin-tin orbital (TB-LMTO) method within local density approximation (LDA) have been reported. Our calculated band structure and density of states (DOS) for the doped systems clearly show that the ground state of the R ¼ Ce2Yb systems are metallic while the R ¼ Lu system (it has completely filled 4f states) is insulating. This insulating phase of Lu 3 Al 5 O 12 is in very good agreement with the experimental results. Our calculations correctly brings out the narrow bandwidth feature of 4f states. Our studies clearly show that the position of the O-2s/p in YAG remains intact while substitution, the O-2p and R-4f energy gap remains almost the same up to near half filling of 4f states ðR ¼ Ce2PmÞ, from then it decreases continuously up to R ¼ Yb and finally it becomes zero for R ¼ Lu (insulator) due to a strong hybridization between the O-2p and Lu-4f states. Our calculated cohesive energy ðE coh Þ per molecule for these systems decreases from R ¼ Ce2Sm (up to half filling of 4f bands) then increases from R ¼ Sm2Tb, decreases from R ¼ Tb2Yb (more than half filling) and finally increases for R ¼ Lu, which is an insulator. This decreasing and increasing trend of E coh is exactly similar to that of the rare-earth elemental solids, indicating that the rare-earth elements in the YAG system plays crucial role in deciding the physical properties of the doped systems. However, there are no experimental results available to our knowledge to compare our results.