The one-photon forbidden excited state in an one-dimensional sigma-electron-conjugated polymer, polysilane, was investigated by means of second-harmonic (SH) generation spectroscopy. It was found that resonant SH peak attributable to a forbidden excited state was observed on the high-energy side of the linear absorption peak and that the SH intensity exhibits a drastic change accompanied with the backbone order-disorder phase transition in alkylpolysilane, This behavior was discussed on the basis of the electron delocalization in their backbone of one-dimensional conjugated polymers and the resonance condition of non-linear optical processes.