High-level multireference configuration interaction plus Davidson correction (MRCI + Q) calculation method was employed to determine the potential energy curves (PECs) of 10 Λ-S states, which come from the first and second dissociation channels of the SbP molecule, as well as 34 Ω states considering the spin-orbit coupling (SOC) effect. By solving the Schrödinger equation for nuclear motion, spectroscopic constants for the ground state X1Σ+ and low-lying excited states were obtained and compared with experimental data. The excellent agreement indicates the reliability of our calculations. Additionally, the calculated spin-orbit (SO) matrix elements of the 13Π and 15Π states with other Λ-S states were analyzed, and the majority of the values in the Franck-Condon region exceed 200 cm-1, indicating strong interactions between these states. What's more, the joint effects of spin-orbit coupling and avoided crossing were discussed in detail, leading to the complex potential energy curves and double-well phenomena observed in the Ω states. Taking forbidden transitions into account, transition dipole moments with the SOC effect are considered. The Franck-Condon factors, Einstein coefficients, and radiative lifetimes for the 13Σ+1 ↔ X1Σ+0+ transition were obtained. Analysis indicates that direct laser cooling of SbP is inappropriate.