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The equilibrium structures of orthorhombic LaCrO3(O-LaCrO3) and rhombohedral LaCrO3(R-LaCrO3) crystals were investigated by using the plane-wave self consistent field (PWSCF) method based on density functional theory (DFT). The optimized lattice parameters for both phases are in accordance with experimental results reported in literature, confirming the reliability of LSDA+U scheme used in the calculations. We have quantificationally investigated the binding energies and electronic properties of these two types of LaCrO3crystals. The negative total energy and binding energies indicate the ground state property and the good structrual stability of O-LaCrO3crystal, which is important for the preparation of nano materials, the synthesis of ceramic materials made of doped O-LaCrO3crytals, as well as their applications in high technology fields, and predict the metastable property of R-LaCrO3crystal. Furthermore, the band structures show that O-LaCrO3is a direct semiconductor with wide energy gap, while R-LaCrO3is an indirect semiconductor with narrow energy gap. The interaction between Cr and O atoms in O-LaCrO3crystal possesses the character of covalent bonding.