In this paper, we study the response properties of multi-photon of NbN superconductor nanowire in superconducting single photon detector (SSPD). We measure the NbN nanowire device's DC characteristics and detection probability for single and multi-photon light pulse signal at a temperature of 3.5 K. The measured results show that the superconducting transition current of superconductor nanowire decreases as light irradiation intensity increases. The photon number detected by SSPD is derived from the slope of detection probability versus light intensity. We find that the detected photon number increases as superconducting nanowire bias current decreases. Moreover, based on quantum optics and hotspot theory, we analyze the mechanism of the multi-photon response of superconducting nanowire semi-quantitatively. This result may be of benefit to understanding SSPD and developing the SSPD with the capability of resolving photon number.