We investigate the response time function of the avalanche photodiode single-ph oton detector for weak laser pulses with different incident photons and present a method to distinguish the incident photon number based on the response time of different photons.The association between the response time of different photons and detection time of weak laser pulse is analyzed theoretically.The tr ansient response time of the single-photon detector under different incident laser power values is investiga ted experimentally.The response time values of one photon,two photons and three photons at the wavelength of 1550nm are achieved to be 10.73±0.22ns,8.75±0.62ns,5.98±1.27ns,respectively, which can be an accurate criterion for photon-number -resolving of week light field.The dependence of photon response time on the change of weak laser pulse detection t ime induced by photon number statistical fluctuation of the single-photon detec tor is also analyzed.