The feasibility of spin-forbidden cooling of the In H molecule is investigated based on ab initio quantum chemistry calculations. The potential energy curves for the X~1Σ_(0~+)~+, a~3Π_~(0~-), a~3Π_(0~+), a~3Π_1, a~3Π_2, A~1Π_1, 1~3Σ_(0~-)~+, and 1~3Σ_1~+states of In H are obtained based on multi-reference configuration interaction plus the Davidson corrections method. The calculated spectroscopic constants are in good agreement with the available experimental data. In addition, the influences of the active space and spin–orbit coupling effects on the potential energy curves and spectroscopic constants are also studied. For Re of a~3Π_(0~-), a~3Π_(0~+), a~3Π_1, and a~3Π_2 states, the error from large active space is small. The potential energy curve of the A~1Π_1state is not smooth for small active space. The spin–orbit coupling effects have great influences on the potential well depth and equilibrium internuclear distance of the A~1Π state. The Franck–Condon factors and radiative lifetimes are obtained on the basis of the transition dipole moments of the a~3Π_(0~+) → X~1Σ_(0~+)~+, a~3Π_1 → X~1Σ_(0~+)~+, and A~1Π_1 → X~1Σ_(0~+)~+ transitions. Our calculation indicates that the a~3Π_1( ν’= 0) → X~1Σ_(0~+)~+(ν = 0) transition provides a highly diagonally distributed Franck–Condon factor and a short radiative lifetime for the a3Π1 state, which can ensure rapid and efficient laser cooling of In H.The proposed laser drives a~3Π_1 → X~1Σ_(0~+)~+ transitions by using three wavelengths. The feasibility of spin-forbidden cooling of the In H molecule is investigated based on ab initio quantum chemistry calculations. The potential energy curves for the X ~ 1Σ_ (0 ~ +) ~ +, a ~ 3Π_ ~ (0 ~ ~ 3Π_ (0 ~ +), a ~ 3Π_1, a ~ 3Π_2, A ~ 1Π_1, 1 ~ 3Σ_ (0 ~ -) ~ +, and 1 ~ 3Σ_1 ~ + states of In H are obtained based on multi-reference configuration interaction plus the Davidson corrections method. The calculated spectroscopic constants are in good agreement with the available experimental data. In addition, the influences of the active space and spin-orbit coupling effects on the potential energy curves and spectroscopic constants are also studied. a ~ 3Π_ (0 ~ -), a ~ 3Π_ (0 ~ +), a ~ 3Π_1, and a ~ 3Π_2 states, the error from large active space is small. The potential energy curve of the A ~ 1Π_1state is not smooth for Small active space. The spin-orbit coupling effects have great influences on the potential well depth and equilibrium internuclear distance of the A ~ 1Π state. The Franck-Condon factor s and radiative lifetimes are obtained on the basis of the transition dipole moments of the a ~ 3Π_ (0 ~ +) → X ~ 1Σ_ (0 ~ +) ~ +, a ~ 3Π_1 → X ~ 1Σ_ (0 ~ +) , and A ~ 1Π_1 → X ~ 1Σ_ (0 ~ +) ~ + transitions. Our calculation indicates that the a ~ 3Π_1 (ν ’= 0) → X ~ 1Σ_ (0 ~ +) ~ + (ν = 0) a highly diagonally distributed Franck-Condon factor and a short radiative lifetime for the a3Π1 state, which can ensure rapid and efficient laser cooling of In H. Proposed laser drives a ~ 3Π_1 → X ~ 1Σ_ (0 ~ +) ~ + transitions by using three wavelengths.