In this work, the potential energy curves of eight low electronic states (X¹Σ⁺, a³Π, A¹Π, b³Σ^-, 2³Π, 1³Σ⁺, 1⁵Σ^-, and 1⁵Π) and twenty-three Ω states of BH molecule, and the transition dipole moments among the \textX^\text1\Sigma_\text0^ + ^ + , \texta^\text3\Pi_\text0^ + , a³Π₁, a³Π₂, and A¹Π₁ states 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 A¹Π₁(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 A¹Π₁(υ′ = 0, 1) have short spontaneous radiation lifetimes. Moreover, the effects of \texta^\text3\Pi_\text0^ + and a³Π₁ states on A¹Π₁(υ′ = 0) ↔ \textX^\text1\Sigma_\text0^ + ^ + (υ′′ = 0) cycle transition can be ignored. Therefore, according to the A¹Π₁(υ′ = 0-1, J′ = 1, +) ↔ \textX^\text1\Sigma_\text0^ + ^ + (υ′′ = 0-3, J′′ = 1, –) cycle transition, we propose to apply one main cooling laser (λ₀₀ = 432.45 nm) and two repumping lasers (λ₁₀ = 479.67 nm and λ₂₁ = 481.40 nm) to laser cooling BH molecules, and evaluation of the cooling effect.