Epoxy/glass fibre composites possess excellent mechanical and electrical properties and are widely utilised in electrical and electronic power equipment. However, the composites exhibit relatively poor thermal conductivity, causing the temperature of the composites to increase during the operation of power equipment, resulting in a significant reduction in the electrical breakdown strength. Although the effects of thermal aging on polymeric materials have been widely studied, its influence on electrical strength mechanisms has not been investigated at the molecular level. In this study, epoxy/glass fibre composite specimens were subjected to accelerated thermal aging treatment for 360 h at 180 °C. Functional groups, molecular chain dynamics, and electrical breakdown are characterised using infrared spectroscopy, dielectric spectroscopy, and breakdown measurement. Subsequently, electrical breakdown mechanism and life prediction of the thermally aged composites are discussed. During thermal aging, the epoxy resin molecular chains undergo continuous oxidation and chain scission, which generate numerous polar functional groups and short chains and an increase in the free volume. This triggers an enhancement in the chain segmental dynamics, thereby significantly reducing the activation energy of the epoxy resin. After 360 h, activation energy decreased from 0.78 eV to 0.67 eV. The DC breakdown voltages of the specimens decreased from 168.28 kV/mm to 134.91 kV/mm. An insulation life prediction model for thermally aged epoxy/glass fibre composites is established based on the time-temperature equivalence theory. The prediction results indicate that the service life of the operational composites is approximately 11.2 years at 353 K, which is consistent with engineering experience.