On the basis of correcting various errors caused by spin-orbit coupling effects, scalar relativity effects, core-valence correlation effects and basis set truncation, the potential energy curves of 10 Λ-S states and 26 Ω states of AlH molecule are calculated by using icMRCI + Q method. The transition dipole moments of 6 pairs of transitions between the \rm X^1\Sigma _0^ + ^ + , \rm a^3\Pi _0^ + , \rm a^3\Pi _1 , \rm a^3\Pi _2 , and \rm A^1\Pi _1 states are calculated by using the icMRCI/AV6Z* theory with the consideration of spin-orbit coupling effects. The spectral and transition data obtained here for AlH molecule are in very good agreement with the available experimental measurements. The findings are below. 1) The transition intensities are relatively strong of the Q(J″) branches for the (0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4) and (1, 5) bands of the A¹Π₁ – \rm X^1\Sigma _0^ + ^ + transition, with the increase of J″; the Einstein A coefficients and vibrational branching ratio gradually decrease, and the weighted absorption oscillator strength gradually increases of Δυ = 0 band, the Einstein A coefficient, vibrational branching ratio, and weighted absorption oscillator strength gradually increase for the Δυ ≠ 0 bands. 2) The radiation lifetimes of A¹Π₁(υ' = 0, 1) increases slowly as the J' increases. 3) The A¹Π₁(υ' = 0 and 1, J' = 1, +) →\rm X^1\Sigma _0^ + ^ + (υ'' = 0–3, J'′ = 1, –) transition of AlH molecule satisfies the criteria for laser cooling of diatomic molecules, that is, the vibrational branching ratio of the highly diagonal distribution, the extremely short radiation lifetimes of the A¹Π₁(υ' = 0 and 1, J' = 1, +) states, and the intermediate electronic states \rm a^3\Pi _0^ + , a³Π₁, and a³Π₂ do not interfere with laser cooling. Therefore, based on the cyclic transition A¹Π₁(υ' = 0 and 1, J' = 1, +) ↔ \rm X^1\Sigma _0^ + ^ + (υ'′ = 0–3, J'' = 1, –), we propose a feasible scheme for laser cooling of AlH molecule. When cooled, 2.541 × 10⁴ photons can be scattered by four pump lasers used in the visible range, which are enough to cool AlH to the ultra-cold temperature, and the Doppler temperature and recoil temperature of the main transition are on the order of μK.