We have measured a spectrum of third-order nonlinear optical susceptibility |x(3)(-3ω;ω,ω,ω)| of σ-conjugated polysilane, poly(di-n-hexylsilane) (PDHS), by means of third-harmonic generation (THG) measurement, in the fundamental photon energy region from 0.56 eV to 2.15 eV. The obtained | x(3)(3ω; ω, ω, ω)| spectrum exhibits three peaks. These peaks are interpreted as the multi-photon resonance enhancement to the one-dimensional exciton states. This exciton model can be applied also to the nonlinear optical response of other conjugated polymers.