The static second hyperpolarizability tensors of H-(C≡C) n -H (n = 3-9, 15) along the molecular axis [γ zzzz (∞)] is much larger than those in the vertical direction [γ xxxx and γ yyyy (∞)], and the hyperpolarizability increases significantly with increasing carbon chain length, which are consistent with the relative order of the polarizability components. For each carbon chain, the frequent-dependent second hyperpolarizability tensors [γ iiii (λ), i = x, y, and z, λ = 1907, 1460, 1340, and 1064 nm] are higher than the static case [γ iiii (∞), i = x, y, and z]. The longer the carbon chain is, the more obvious difference between frequent-dependent and static values is, indicating that the frequency-dispersion of molecular second hyperpolarizability becomes more remarkable with the increase of chain length. The resonance effect of the second hyperpolarizability induced by incident light amplifies steadily with the increase of light frequency.