Two-photon absorption spectra are difficult to observe using direct absorption spectroscopy especially in the near-infrared region. Cavity ring-down spectroscopy is a promising absorption spectroscopy technique which has been widely applied to linear and saturated single-photon absorption spectra. In the present study, we report the observation of a possible two-photon absorption in the near-infrared using cavity ring-down spectroscopy, namely a two-photon resonance of methane. Using an optical frequency comb, the single-photon wavenumber of the double-quantum transition has been determined to be 182 207 682.645 MHz with a standard deviation of 75 kHz.