The TianQin Project is aiming at gravitational wave (GW) detection in space. TianQin GW observatory comprises three satellites orbiting on 1 x 10(5) km Earth orbits to form an equilateral-triangle constellation. In order to minimize the variations in arm lengths and breathing angles, the satellites must be launched and adjusted precisely into an optimized orbit. Therefore, satellite laser ranging must be used to enhance the precision of satellite orbit determination. To develop the capability of satellite laser ranging for TianQin's orbit, the TianQin Laser Ranging Station has been designed and constructed to perform high-precision laser ranging for TianQin satellites and lunar laser ranging as well. Applying a 1064 nm Nd: YAG laser with 100 Hz repetition frequency, 80 pico-second pulse duration, and 2 x 2 array of superconducting nanowire single-photon detectors, we have obtained the laser echo signals from the five lunar retro-reflector arrays, and the measurement data have been packaged into 234 normal points (NPs), including a few data measured during the full-moon lunar phase. Each NP is calculated from continuous measurement for about ten minutes and the statistical error of the NPs is about 7 mm (1 sigma).