We report the simple detection method of the small hydrocarbons, methane and ethane, by continuous-wave cavity ring-down spectroscopy near 1.67 ${mu}m$ using an external cavity diode laser. The absorption lines of methane between 6002.48 $cm^{-1}$ and 6003.37 $cm^{-1}$ and ethane between 5955.65 $cm^{-1}$ and 5956.4 $cm^{-1}$ have been resolved and employed for the gas detection. The largest absorption cross sections were found to be 6.5$ imes10^{-20}cm^2$ and 7.4$ imes10^{-21}cm^2$ for methane and ethane, respectively, in each spectral range. The minimum detectable absorption limit of our spectrometer was 4.8${ imes}10^{-9}cm^{-1}$/$sqrt{Hz}$, which corresponds to the detection limits of 3 ppb/$sqrt{Hz}$ and 27 ppb/$sqrt{Hz}$ for methane and ethane, respectively. The near-IR continuous-wave cavity ring-down spectroscopic detection method of the small hydrocarbons can be applied for medical diagnosis and environmental monitoring as a fast and convenient method.