Based on the satellite laser ranging （SLR） system at Shanghai Astronomical Observatory， the laser output energy was increased by using the 885 nm end-pumped Nd：YAG amplification. Each pulse of 10 kHz was obtained near-equal amplitude by controlling the pump gain current， Nd：YAG crystal cool water temperature and building time of regeneration amplification. An average power of 6 W picosecond laser in a wavelength of 532 nm was obtained at a repetition rate of 10 kHz with the divergence angle of 0.6 mrad， pulse width of 30 ps， a beam quality M² of 1.2. The noise levels for single photon detector at each repetition rate of 1 kHz， 2 kHz， 4 kHz， 5 kHz， 6.25 kHz， and 10 kHz was measured and analyzed respectively. The relationship between the false alarm probability and the ranging gating is obtained. The relationship between the number （N） of noise photons and the repetition rate （f） is N=743784.76+431.08f， and the relationship between the false alarm detection probability （P） and the ranging gated （Δt） at the repetition rate of 10 kHz is P(△t)=1-e-5054584.76×△t， and also the function of the number of laser echoes with noise， laser energy and repetition are obtained， which is beneficial to design the SLR system. Therefore， it realizes the satellite laser ranging in all day， and the farthest distance was to the synchronous orbit of Beidou Compassi6b satellite.