The potential energy curve (PEC) of b4Σ- electronic state of the SO+ cation is calculated using the internally contracted multireference configuration interaction approach with the Davidson modification (MRCI+Q) for internuclear separations from 0.103 to 1.083 nm. The basis set used is a correlation- consistent aug-cc-pV5Z basis set. The spin-orbit coupling effect on the spectroscopic parameters is taken into account by the state interaction approach with the full Breit-Pauli operator with all-electron basis set, aug-cc-pCVTZ. To improve the quality of PEC and spin-orbit coupling constant, core-valence correlation and relativistic corrections are included. Core-valence correlation correction is calculated using a cc-pCVTZ basis set. Relativistic corrections are included by the third-order Douglas-Kroll Hamiltonian approximation at the level of a cc-pV5Z basis set. At the MRCI+Q/aug-cc-pV5Z+CV+DK level, the spin-orbit coupling constant of the SO+ (b4Σ-1/2,3/2) is 1 cm-1 when the aug-cc-pCVTZ basis set is used for the spin-orbit coupling calculations The spectroscopic parameters are determined and compared with those reported in the literature. Excellent agreement is found between the present results and the measurements. The vibrational level G(v) inertial rotation constant Bv and centrifugal distortion constant Dv are predicted for each vibrational state of the b4Σ- electronic state by solving the ro-vibrational Schrödinger equation of nuclear motion using Numerov's method and those of the first 2 vibrational states are reported for the non-rotation SO+ cation. Comparison with the measurements demonstrates that the present vibrational manifolds are both reliable and accurate. They should be good predictions for future experimental or theoretical research.