The multi-reference configuration interaction (MRCI) method in quantum chemistry is used to investigate the BP+ at the level of aug-cc-pVQZ basis set. The potential energy curves of 6 Λ-S states of BP+ radical are obtained, which can be correlated to the dissociation limit B+(1Sg)+P(4Su), B+(1Sg)+P(2Du) and B+(1Sg)+P(2Pu). In order to get the accurate potential energy curves, the Davidson correction (+Q) and scalar relativistic effect are taken into consideration. Analyses of the electronic structures of Λ-S states demonstrate that the Λ-S electronic states are multi-configurational in nature. The spin-orbit interaction is considered for the first time sofar as we have, which makes 6 Λ-S states split to 10 Ω states. The calculation results show that the crossing between the Ω states of the same symmetry can be aveided. Then the spectroscopic constants of the bound Λ-S and Ω states are obtained by solving the radial Schrödinger equation with the program LEVEL8.0 according to the MRCI wave functions. By comparing with available experimental results, the spectroscopic constants of ground states are in good agreement with the available theoretical values. The remaining computational results in this paper are reported also for the first time.