A high-precision quantum chemistry ab initio multi-reference configuration interaction method with aug-cc-pVQZ basis sets has been used to calculate the four states of BP molecule. The four -S states are X3, 3-, 5 and 5-, which are correlated to the lowest dissociation limit of B(2Pu)+P(4Su). Analysis of the electronic structures of -S states shows that the -S electronic states are essentially multi-configurational. We take the spin-orbit interaction into account for the first time so far as we know, which makes the four -S states split into fifteen states. 30+ state is confirmed to be the ground state. The SOC effect is essential for the BP molecule, which leads to the avoided crossings for 0+ and 1 states from X3 and 3-. Based on the PECs of -S and states, the accurate spectroscopic constants are obtained by solving the radial Schrdinger equation. The spectroscopic results may be conducive to further research on BP molecule in experiment and theory.