Abstract: Some electronic structure properties of the densities of energy states, Fermi Energies and Energy Gaps in the systems of RE₄Cr₂O₉(RE=La,Pr,Nd,Sm,Gd,Dy,Ho,Er) are calculated by means of SCF-Xa-SW methods. Compared with the conductivity properties of RECrO₃, the relations between the electronic structure and conductivities are studied. The result shows that,with the increase of the atomic number of RE, their densities of energy states increases (mainly due to f electrons) and the non-f electrons decreases gradually. Therefore the conductivity has no relation with that of f electrons of RE. This is the main reason that the conductivity decreases with the increase of atomic number of RE.