High-precision space debris measurement can provide more accurate real-time information of debris targets and enhance the effectiveness of satellite avoidance and early warning of space debris. The satellite laser ranging (SLR) and space debris laser ranging (DLR) experiments were carried out by using picosecond laser with pulse energy of 1.2 mJ and repetition frequency of 1 kHz. The atmospheric propagation characteristics of picosecond laser were studied and analyzed. The cooperative satellites measured distances from 500 km to 36000 km with ranging accuracy better than 2 cm. The maximum distance of space debris target measurement is 1620.5 km, the radar cross section (RCS) is 2.41 m2, and the ranging accuracy reaches 10.64 cm. It is realized that a single laser system can carry out centimeter-level precision ranging of cooperative targets and space debris observation. This is the first time in the world to use high repetition frequency and low power laser ranging system to achieve high precision measurement of space debris targets, reflecting the advantages of picosecond laser and high altitude large aperture telescope measurement, providing an effective way for space debris laser ranging system site selection and space debris monitoring capability enhancement.