We demonstrate a photon-counting chirped amplitude modulation (CAM) light detection and ranging (lidar) system incorporating a superconducting nanowire single-photon detector (SNSPD) and operated at a wavelength of 1550 nm. The distance accuracy of the lidar system was determined by the CAM bandwidth and signal-to-noise ratio (SNR) of an intermediate frequency (IF) signal. Owing to a short dead time (10 ns) and negligible dark count rate (70 Hz) of the SNSPD, the obtained IF signal attained an SNR of 42 dB and the direct distance accuracy was improved to 3 mm when the modulation bandwidth of the CAM signal was 240 MHz and the modulation period was 1 ms.