The two-photon absorption coefficient spectra of indirect transitions in silicon have been measured using a picosecond Nd:YAG pulsed laser pumped optical parametric generator, whose wavelength being tunable. By employing the pulsed laser with the photon energy less than the indirect energy gap of silicon, the photovoltaic response between two electrons of the silicon photovoltaic diode has been detected significantly. The peak intensity of the pulsed photovoltaic response shows a quadratic dependence on the incident intensity. This suggests a typical two photon absorption process. A relationship between the pulsed photovoltaic response and the incident intensity has been established with an equivalent RC circuit model to derive the two-photon absorption coefficient, and the spectra can also be obtained by turning the incident wavelengths. The results show that when the incident photon energy change from 0.689 eV to 0.912 eV, the two-photon absorption coefficient increase form 0.42 cm/GW to 1.17 cm/GW. The mechanism for the two-photon absorption coefficient increasing with the incident photon energy can be attributed to the electrons excited from valance band finding an increasing availability of conduction-band states as the photon energy increase from Eig/2 to near Eig. This photon frequency dependence of the two-photon absorption coefficient has been fairly interpreted by the Dinu model.