In this work, the potential energy curves of eight low electronic states (X ¹Σ ⁺, a ³Π, A ¹Π, b ³Σ ^-, 2 ³Π, 1 ³Σ ⁺, 1 ⁵Σ ^-, and 1 ⁵Π) and twenty-three Ω states of BH molecule, and the transition dipole moments among the \textX^\text1\Sigma_\text0^ + ^ + , \texta^\text3\Pi_\text0^ + , a ³Π ₁, a ³Π ₂, and A ¹Π ₁states are calculated by using the internally contracted multireference configuration interaction (icMRCI) method. In order to obtain the accurate potential energy curve, the errors caused by single and double electron excitation, core-valence correlation effects, relativistic effects and basis set truncation are corrected. The spectral and transition data of BH molecule are in good agreement with the available theoretical and experimental data. The calculation results show that the A ¹Π ₁( υ′= 0-2, J′= 1, +) → \textX^\text1\Sigma_\text0^ + ^ + ( υ′′= 0-2, J′′= 1, –) transition has large Einstein A-coefficient, weighted absorption oscillator strength, and highly diagonal vibrational branching ratio R _{υ′υ′′}, and the excited state A ¹Π ₁( υ′= 0, 1) have short spontaneous radiation lifetimes. Moreover, the effects of \texta^\text3\Pi_\text0^ + and a ³Π ₁states on A ¹Π ₁( υ′= 0) ↔ \textX^\text1\Sigma_\text0^ + ^ + ( υ′′= 0) cycle transition can be ignored. Therefore, according to the A ¹Π ₁( υ′ = 0-1, J′= 1, +) ↔ \textX^\text1\Sigma_\text0^ + ^ + ( υ′′ = 0-3, J′′ = 1, –) cycle transition, we propose to apply one main cooling laser ( λ ₀₀= 432.45 nm) and two repumping lasers ( λ ₁₀= 479.67 nm and λ ₂₁= 481.40 nm) to laser cooling BH molecules, and evaluation of the cooling effect.