In order to investigate the characteristics of the package and fiber coupling of a Superconducting Nanowire Single-photon Detector (SNSPD), the SNSPD was successfully built up in our laboratory. Experiments show that the quantum efficiencies of the detector under different light wavelengths are 6%@1310nm and 3%@1550nm when the dark count rate is 100 Hz. Then, as the distance(gap) between SNSPD and optical fiber would be changed due to the thermal stress during cooling, and would cause a misalignment, two kinds of fiber coupling methods to modulate the gap at room temperature were proposed. Finally, by altering the wavelength of the input light, the exact values of the gap at different temperatures were measured and then the influence of temperature on the gap were figured out by an experiment. The experimental results indicate that decreases of the gap for the two packages are 4.1 μm and 17 μm when the temperature dereases 270 K. Based on the analysis of package material and structure, the gaps at both room and low temperature were calculated theoretically. The result fits well with that of the experiments and it may offer some references to the design of new package and fiber coupling in the future.