In the present study, the time-temperature dependencies of fracture toughnesses, K-Ic, were investigated for bisphenol-A type epoxy resin and silica particulate-filled epoxy composite. Glass transition temperature, T-g, and Angell's fragility parameter, m, derived from thermo-viscoelasticity, were used to characterize the epoxy resin and its composite, which were cured under various conditions. We conducted a fracture toughness test at various temperatures and displacement rates. The results revealed that the K-Ic, of the epoxy resin and composite depend on both temperature and time. The K-Ic follows a time-temperature equivalent principle. We found that the temperature-time dependence of K-Ic, depends on m, although brittle-ductile transition is governed by alpha-relaxation phenomena expressed by T-g.