The electronic structure, magnetic and electric properties, and lattice stability of multiferroic BiMnO 3 as a typical system in perovskite Bi transition-metal oxides (BiMO 3) are studied from first principles. It is demonstrated theoretically for the first time that the orbital ordering within the Mn e g orbitals is actually realized in BiMnO 3, being consistent with crystallographic data, and plays a crucial role in the appearance of ferromagnetism. Total-energy calculation shows the ferromagnetic state is indeed stabilized. Electrical polarization of BiMnO 3 is also estimated based on the Berry phase theory. Lattice instability to off-centred displacement, which is driven by strong covalent bonding between Bi 6p and O 2p states, is found to be rather common in the BiMO 3 series.