We report europium (Eu)-induced changes in the π-band of graphene (G) formed on the 6H-SiC(0001) surface by a combined study of photoemission measurements and density functional theory (DFT) calculations. Our photoemission data reveal that Eu intercalates upon annealing at 120 °C into the region between the graphene and the buffer layer (BL) to form a G/Eu/BL system, where a band gap of 0.29 eV opens at room temperature. This band gap is found to increase further to 0.48 eV upon cooling down to 60 K. Our DFT calculations suggest that the increased band gap originates from the enhanced hybridization of the graphene π-band with the Eu 4f band due to the increased magnetic ordering upon cooling. These Eu atoms continue to intercalate further down below the BL to produce bilayer graphene (G/BL/Eu) upon annealing at 300 °C. The π-band stemming from the BL then exhibits another band gap of 0.37 eV, which appears to be due to the strong hybridization between the π-band of the BL and the Eu 4f band. The Eu-intercalated graphene thus illustrates an example of versatile band gaps formed under different thermal treatments, which may play a critical role for future applications in graphene-based electronics.