We demonstrate laser-ranging results for non-cooperative targets at ranges of 237 m and 19 km using superconducting nanowire single-photon detectors (SSPD). We upgrade the kilohertz rate laser-ranging system with a newly developed SSPD module, and the equivalent detection diameter is enlarged to 50 mu m with a fiber and micro-lenses. Both retroreflectors and non-cooperative surfaces of aluminum foil, a solar panel, and a concrete panel at distances of 237 m and 19 km, whose echoes are of single-photon level, are ranged with sub-centimeter precision. Experimental signal-to-noise ratio curves with the product of quantum efficiency and system transmittance are obtained, which indicates that our system, with an average laser power of 0.8 W and a receiving aperture of 1.2 m, may be capable for space debris ranging at a distance of 800 km. This work suggests that SSPDs have the potential to be used for space debris surveillance.