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• The PECs of the 6 Λ-S states have been calculated. • The PECs of the 11 Ω states arising from 6 Λ-S states have been calculated. • TDM of spin forbidden transition from different multiplicity were investigated. • Interference of the intermediate a ʹ3Σ+ on direct laser cooling has been studied. High-level ab initio calculation of silver hydride (AgH) is performed by utilizing the internally contracted multi-reference configuration interaction plus Davidson correction method. A total of 6 Λ-S states and 11 Ω states from low-lying electronic states are computed in consideration of the spin-orbit coupling (SOC). The spectroscopic constants of bound states are determined and are in good agreement with the results of the available literature. A large aug-cc-pwCV5Z-PP basis set for Ag atom is applied during the calculations. The transition dipole moment (TDM) of spin forbidden transition between different multiplicity, caused by SOC effect, are computed based on Breit-Pauli operator. Particularly, the TDM of spin forbidden transitions between triplet a ʹ3Σ+, a 3Π, b ʹ3Σ+ and singlet X 1Σ+, A 1Σ+, C 1Π is studied and discussed. Finally, the interference of laser directly cooling by intermediate a ʹ3Σ+ states due to SOC was investigated based on the obtained TDM parameters. It proves that the perturbation from a ʹ3Σ+ state could be neglected in the laser cooling process. [ABSTRACT FROM AUTHOR]