As a special optical phenomenon，the Goos-Hänchen (GH) shift is closely related to the construction material for a certain optical structure. For the dielectric /superconductor /dielectric structure，the variation curves of the GH shift with the incident angle，the wavelength of light and the thickness of the superconducting material layer are given when the superconducting material is the near-zero refractive index material. The results show that the variation of GH shift with the above-mentioned parameters is related to the threshold wavelength which is defined as the wavelength at which the refractive index of the superconducting material is zero. It is found that there is a certain difference for the GH shift when the wavelength is greater than or less than the threshold wavelength. Near-zero refractive index materials have a wide application in the field of photonics. The calculation results provide a useful reference for the research and development of new photonic devices. The paper also helps undergraduates to understand the concept of near-zero refractive index and the GH shift of superconducting materials in the near-zero refractive index region.