•Second hyperpolarizabilities γ of transition-metal dinuclear complexes.•Axial ligand effects on the diradical character (y) dependence of the γ.•The axial ligand coordinated complexes show larger y values than the bare system.•Open-shell dσ electrons enhance the |γ| as compared to the bare system.•Large negative γ values emerge in the small metal–metal bond-length region. We investigate the axial ligand effects on the diradical character (y) dependences of the second hyperpolarizabilities (γ) of transition-metal dinuclear complexes, Mo(I)2(CO)2, with different bond lengths (R) using the spin-unrestricted coupled-cluster method. Mo(I)2(CO)2 exhibits intrinsic y–γ correlation and dominant dσ-electron contribution to the maximum γ (γmax), which are also observed in the bare dinuclear analogs. The axial-ligand coordination to Mo(I)2 is found to cause the increase of the diradical character of the dσ orbital, the emergence of large negative γ for small R, and an enhancement of |γmax| by a factor of ∼30 as compared to the bare analogs.