Recycled construction and demolition (C&D) waste can reduce the rebuild cost, and is environmentally friendly when recycled asphalt pavement (RAP) aggregate constitutes the main part. This paper investigated the mechanical performance of RAP concrete, and the applicability of RAP in road base layers also was discussed. Several mechanical laboratory tests were selected, including the unconfined compressive-strength, splitting-strength, and compressive-resilience modulus tests. The RAP concrete had a good road performance in a cold region, which was proved by the temperature-shrinkage test, dry-shrinkage test, freeze–thaw-cycle test, and water-stability test. Based on various cement dosages from 3.5% to 5.5% in RAP concrete mix design, three RAP aggregate replacement ratios (30%, 40%, and 50%) were selected to study the variation of mechanical properties with increasing curing time, and the optimal aggregate substitute ratio was determined. A scanning electron microscope (SEM) was used to observe the inner-structure interface between the asphalt binder and cement stone. A numerical model is presented to simulate the RAP compressive strength with respect to the effect of multiple parameters. The research results can provide a technical reference for RAP use in the reconstruction and expansion of low-grade highway projects.