We have demonstrated the $1.6\mu \text{m}$ cw modulation hard-target differential absorption lidar system for ${\text{CO}}_2$ sensing. In this system, ON and OFF wavelength laser lights are intensity modulated with cw signals. Received lights of the two wavelengths from the hard target are discriminated by modulation frequencies in the electrical signal domain. The optical circuit is fiber based, and this makes the system compact and reliable. It is shown that a stable ${\text{CO}}_2$ concentration measurement corresponding to a fluctuation of 4 ppm (rms) (ppm is parts per million) has been achieved in 32 s measurement intervals and the 1 km path.