The electronic properties of multiferroic BiFeO3 with paraelectric paramagnetic phase at high-temperature and ferroelectric antiferromagnetic phase are calculated using density functional theory with spin-polarized generalized-gradient approximation (GGS) and plane wave pseudopotentials. study of Born effective charges shows that the greatest contributor to the ferroelectric distortion is Bi atoms' displacement. We obtained very large theoretical electric polarization, which agrees very well with the results of thin-film test. The calculation shows that BiFeO3 ground state has G type anti-ferromagnetic order and the theoretical magnetic moments of Fe ion accord with experimental values. After ferroelectric phase transformation, the chemical bond changes much due to Bi-6s and Bi-6p state charge transfer, and the effect of Bi-6s electrons becomes more pronounced. Partial density of states calculation indicates that the energy split between bonding orbit of Bi-6p state and anti-bonding orbit is bigger than that between other electronic states, by which covalent bond between Bi-6p state and O-2p state is strengthened, which is the origin of off-center displacement. Thus the discussion about the BiMnO3 is testified. Bi-6s state is polarized due to the static electric repulsion, but does not take part in the hybridization of Bi-6p and O-2p electrons. The charge transfer originates from its weak covalent interaction with the O-2s, 2p orbits, by which the Bi-6s state electronic polarization is reinforced. This kind of covalent interaction helps the relative replacement of Bi-O, which is the reason for the strong systemic electric polarization.