A comprehensive theoretical study on the low-energy electronic states of superoxide anion (\textO_2^ - ) is carried out, focusing on the influence of spin-orbit coupling (SOC) on these states. Utilizing the complete active space self-consistent field (CASSCF) method combined with the multireference configuration interaction method with Davidson correction (MRCI+Q) and employing the aug-cc-pV5Z-dk basis set that includes Douglas-Kroll relativistic corrections, the electron correlation and relativistic effects are accurately considered in this work. This work concentrates on the first and second dissociation limits of \textO_2^ - , calculating the potential energy curves (PECs) and spectroscopic constants of 42 Λ-S states. After introducing SOC, 84 Ω states are obtained through splitting, and their PECs and spectroscopic constants are calculated. Detailed data of the electronic states related to the second dissociation limit are provided. The results show excellent agreement with those in the existing literature, thus validating the reliability of the method. This work confirms through calculations with different basis sets that the double-well structure of the \texta^4\Sigma _\textu^ - state originates from avoiding crossing with the 2^4\Sigma _\textu^ - state, and finds that the size of the basis set can significantly affect the depth of its potential well. After considering SOC, the total energy of the system decreases, especially for the states with high orbital angular momentum (such as the 1^2\Phi _\textu and 1^4\Delta _\textg states), leading to energy level splitting and energy reduction, while other spectroscopic constants remain essentially unchanged. These findings provide valuable theoretical insights into the electronic structure and spectroscopic properties of \textO_2^ - , present important reference data for future research in fields such as atmospheric chemistry, plasma physics, and molecular spectroscopy. The datasets provided in this work are available from https://doi.org/10.57760/sciencedb.j00213.00076.