A reasonable dissociation limit of B″3Πu state of molecular sulfur (S2) has been derived,and a potential energy curve of B″3Πu and X3Σ-g states of S2 has been calculated by using Gaussian 94 QCISD(T) method and the 6-311++G** basic set function.The murrell-Sorbie potential energy function and spectrum constants are given.Because B″3Πu state overlap extensively with B3Σ-u state in the repulse branch and B″3Πu and X3Σ-g states have the same dissociate limits,they have an overlap in the attract branch.In this paper,the interaction characteristics of B″3Πu,B3Σ-u and X3Σ-g states have also been discussed.