We study the effect of the light rare earth ions La, Ce, Pr, and Nd on electronic structure, structural properties, magnetic states, and ferroelectric properties of BiFeO3 using density functional theory within GGA + U method. The supercell of 40 atoms is considered for four phases: R3c, Pnma, Pn2 (1) a, Pbam. We show that, among potential phases, the R3c-G structure of BiFeO3 where one Bi substituted by one of the studied rare-earth elements has the minimal total energy. We predict the values of spontaneous electric polarization in RE-doped BiFeO3 to be above 80 mu C cm(-2) and a non-zero values of the magnetic moments in RE-doped BiFeO3 for R3c-G phase of the studied systems. Upon introduction of a rare-earth ion to a Bi site, the total magnetic moments are 0 mu(B), 0.99, 1.99, and 2.98 mu(B) f.u.(-1) for La, Ce, Pr, and Nd substitution, respectively. The results of total energy calculations show that the Pn2 (1) a and Pnma phases of the BiFeO3 with Ce or Pr substitution of Bi occur on the same energy scale. This close energy scale suggests a coexistence of these phases beyond T = 0 K or under other conditions.