ABSTRACTThe band structures, density of states and optical properties of trigonal and hexagonal structures of BiFeO3 (BFO) were calculated by density functional theory (DFT) pseudo-potential plane-wave method and generalized gradient approximation (GGA). The calculated band structure of hexagonal exhibits an indirect band-gap with an energy gap of 2.606 eV, which is larger than that of trigonal structure (direct band-gap around 2.401 eV). Ferromagnetism and ionicity of hexagonal structure are better than that of trigonal. From the spectrogram of absorption and conductivity, it is found that the absorption process of BFO includes lattice vibration absorption and intrinsic absorption.