Hybrid materials involving epoxies with different numbers of reactive groups have been prepared to determine the molecular design of epoxies with high fracture toughness at cryogenic temperatures. To answer the opponent demands, that is, strong and flexible chains, hybrid materials were proposed. Two types of epoxy resin with different numbers of epoxy groups were mixed and cured by changing the mixing ratio. Fracture toughness, flexural strength, dielectric loss tangent, and thermal contraction of the hybrid epoxy resins were measured down to cryogenic temperatures. A hybrid material with high fracture toughness, even at liquid helium temperature, was successfully developed and hence the molecular design orientation was confirmed to be possible.