Insulating materials used in the superconducting magnets of fusion reactors are exposed to cryogenic temperatures, intense radiations, and strong electromagnetic forces. In the experimental fusion reactor ITER, resin mixed with epoxy resin (EP) and cyanate ester (CE) (CE content: 40 wt.%) is used as a matrix of glass reinforced plastics (GFRP) as an insulating material to maintains mechanical strength and insulating performance in such environments. This composition ratio is basically determined by strength tests at room temperature or liquid nitrogen temperature, so the study at liquid helium temperature is required. In this study, the effects of the resin composition of GFRP on interlaminar shear stress (ILSS) at room temperature, liquid nitrogen temperature, and liquid helium temperature before and after γ-ray irradiation were evaluated. The ILSS after γ-ray irradiation of EP showed a maximum value at liquid helium temperature, while the addition of CE caused the ILSS after irradiation to show a maximum value at liquid nitrogen temperature. It was also shown that the temperature dependence of the ILSS decreased with increasing CE content. The results showed that the addition of CE to EP contributes to the improvement of radiation resistance, but excessive addition of CE promotes embrittlement at LHeT.