We have demonstrated direct-comb molecular spectroscopy in which an individual-comb mode is resolved by heterodyne detection with a continuous-wave (cw) laser. This simple, fast, and sensitive technique was demonstrated for atomic spectroscopy in [ Appl. Phys. Lett.101, 051105 ( 2012)], but is more suitable for molecular spectroscopy. Four rotation-vibration transitions of methane have simultaneously been recorded in a Doppler-limited resolution using a spectrally broadened comb based on an Er-doped fiber laser and a cw 1651-nm distributed-feedback laser diode. Even though the power level of the comb modes and the sample absorption are weaker than those of the previous studies, in this work the cw laser frequency is stabilized to one of the comb modes, and the data are thereby averaged for extended periods of time, resulting an improvement in sensitivity.