A steady magnetization precession induced by spin-torque was studied in magnetic tunnel junctions with an Fe-rich CoFeB free layer under a perpendicular magnetic field. The Fe-rich CoFeB free layer showed a low critical current (Ic) for spin-torque induced switching. The low value of I c for the Fe-rich CoFeB free layer enabled us to observe the spin-torque induced rf oscillation even at a low dc bias current (I dc). The oscillation frequency increased with increasing I dc, indicating the out-of-plane precessional mode. Owing to the perpendicular magnetic anisotropy in the Fe-rich CoFeB free layer, the large relative angle between the free and pinned layers was achieved under the perpendicular magnetic field. The out-of-plane precession of the magnetization and the large relative angle resulted in the large rf output power of 175 nW.