The B3u- state of O2 molecule is an upper state of the most strongly allowed triplet-triplet (B3u-X3g-) absorption, the Schumann-Runge (SR) transition, which plays a crucial role in protecting the earth from suffering UV radiation. Photo-dissociation of O2 molecule in the SR transition is the major source of odd oxygen (O and O3) in the stratosphere. Comprehensive knowledge of the electronic states, especially their potential energy curves (PECs), is necessary to understand those phenomena. In this paper, we calculate the PEC of B3u- state of O2 by using the internally contracted multi-reference configuration interaction including Davison correction method, which is denoted by icMRCI+Q, and utilize the complete active space self-consistent field (CASSCF) function as a reference function. The calculation is implemented in the MOLPRO suite of codes. Firstly, we carry out the state-averaged (SA) calculation on the four lowest states, A'3u, B3u-, 23u and 23u- states, which are in the same irreducible representation of symmetric group. The active space of CASSCF consists of full valence space. The augmented correlation-consistent aug-cc-pV5Z basis set is used. The results show that the PEC of B3u- state does not displays double well structure, which is contradictory to Liu's result (Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 2014 124 216). By analyzing the PEC structure, we find that the double well of Liu's result comes from the root flipping, that is, the PEC interchange from B3u- state into 23u state. In our case the root flipping is avoided by the SA calculation. Secondly, in order to ensure that the most important configurations are included in the reference function, we calculate the PEC of B3u- state of O2 molecule at CASSCF/aug-cc-pVTZ level by changing the active space. We find that the bound well of the PEC will not appear unless the active space includes 2u orbital which is beyond the full valence space. That means that the Rydberg configurations including 2u orbital play a crucial role in forming the bound well. And the result is further improved by adding into the active space another two orbitals 4g and 4g whose orbital energies are both less than 2u. Finally, we add the Rydberg configurations into the multi-reference configuration function by putting 2u, 4g, 4u into the active space and then carry out the calculation at an icMRCI+Q/aug-cc-pVTZ level. The obtained B3u- state PEC and its spectroscopic constants are in good agreement with the experimental data compared with previous results. Moreover, the process we determine the reference configurations is useful for making accurate calculation at an MRCI level on other species.