The electronic structure, magnetism, and dielectric functions of BiFeO3 with intrinsic vacancies, including Bi-, Fe-, and O-vacancies (denoted as VFe, VBi, and VO, respectively) are investigated using the first-principles density functional theory plus U calculations. It is revealed that the structural distortions associated with those vacancies impose significant influences on the total density of state and magnetic behaviors. The existence of VBi favors the excitation of the O2p state into the band gap at 0.4 eV, while the O2p and Fe3d orbitals are co-excited into the band gap around 0.45 eV in VFe. Consequently, a giant net magnetic moment of 1.96 μB is generated in VFe, and a relatively small moment of 0.13 μB is induced in VBi, whereas VO seems magnetically inactive. The giant magnetic moment generated in VFe originates from the suppression of the spatially modulated antiferromagnetic spin structure. Furthermore, VFe and VBi have strong influences on dielectric function, and induce some strong peaks to occur in the lower energy level. In contrast, VO has a small effect.