The potential energy curves of eight states (X¹Σ⁺, a³Π, A¹Π, 1³Σ⁺, b³Σ^-, 2³Π, 1⁵Σ^- and 1⁵Π) corresponding to the two lowest dissociation limits B(²P_u)+X(²S_g) and B(⁴P_g)+X(²S_g) of BX (X = H, D) molecules are calculated based on the correlation consistent basis sets aug-cc-pV6Z using the high-precision multi-reference configuration interaction (MRCI) method. The radial Schr?dinger equation is solved and the spectral constants of molecular Λ-S bound states are fitted using LEVEL8.0 program. Furthermore, the transition dipole moments, Franck-Condon factor and vibrational level radiation lifetimes of A¹Π-X¹Σ⁺ are calculated. Finally, according to the calculation results, the laser cooling scheme of the electronic transition system is developed, which lays a theoretical foundation for further study of BX (X = H, D) molecular spectral characteristics.