The geometric and electronic structures of rare earth metallofullerenes Eu@C72 were investigated using density functional theory (DFT) within a generalized gradient approximation (GGA). The geometric optimization revealed that the most favorable endohedral site for Eu is off-center along the C2 axis on the sigma(v) plane pointing to the (5, 5) bond at the fusion of two pentagons. Calculations for electronic structures show that two 6s electrons in Eu transfer to the lowest-unoccupied-molecular orbitals of C72 while 4f electrons remain in Eu.