The average content of reclaimed asphalt pavement (RAP) materials in asphalt mixtures for new pavements is around 22% in the current paving practices in the United States. Increasing this content has significant economic and environmental benefits. This study explored the approach of producing asphalt mixtures with 100% RAP materials by adding a small percentage of epoxy asphalt. Specimens of 100% RAP mixtures with low contents of epoxy asphalt were fabricated and evaluated in the laboratory for their properties related to pavement performance, including Marshall stability and flow, indirect tensile strength, resistance to moisture damage, resistance to fatigue damage, and fracture resistance. The results showed that the specimens made of 100% RAP materials selected in this study without a new binder or rejuvenator had low workability and high Marshall stability and indirect tensile strength but poor resistance to moisture damage and fatigue damage. A low percentage (0.5 to 2%) of epoxy asphalt significantly improved the resistance to moisture and fatigue damage of the 100% RAP mixture, and this improvement increased with the epoxy asphalt content. The fracture resistance of the 100% RAP mixture was also significantly improved by a low dosage of epoxy asphalt at a low temperature (8 °C), but the improvement was less significant at a moderate temperature of 25 °C.