A multi-frequency differential absorption lidar incorporating a tunable laser and an optical frequency comb is demonstrated for precise spectrum analysis of atmospheric gas. The single frequency tunable laser is stabilized by locking to the optical frequency comb, with a standard deviation of 0.5 MHz. To achieve a high signal-to-noise ratio, a multi-mode superconducting nanowire single-photon detector with an active-area diameter of 50 µm, a quantum efficiency of 31.5%, and dark noise of 100 counts per second is implemented, which enables to avoid the need for high energy lasers. In the experiment, the range-resolved spectrum of atmospheric mixture gases (CO2 and HDO) in a region of 1572.2 - 1572.45 nm is obtained. Results show different partially overlapped absorption of two gases in different seasons, with a stronger influence of HDO on CO2 in summer than in winter. The interactions are taken into account by separating the mixture absorption spectrum (one CO2 line and two HDO lines) with triple-peak Voigt fitting. The retrieved concentrations over 6 km with a range resolution of 120 m and a time resolution of 10 min are compared with in-situ sensors. The uncertainties of the retrieved concentrations are as low as 6.5 µmol/mol (ppm) and 1×10-3 g/kg for CO2 and HDO, respectively.