In Cuba, tons of construction and demolition waste (CDW) are generated during urban construction and reconstruction activities every year. The use of CDW, such as recycled concrete aggregates (RCA) and reclaimed asphalt pavement (RAP), in pavement construction is a viable solution to preserve the consumption of natural aggregates (NA), and to minimize the impact of landfill. The main objective of this work is to obtain a 5–10 mm aggregate fraction of RCA and RAP, to obtain an appropriate recycled coarse aggregate for manufacturing hot mix asphalt (HMA). Each source of RCA, RAP and NA, and the combinations RCA/RAP (0/100, 25/75, 50/50, 75/25 and 100/0) were characterized (moisture, asphalt content of RAP, specific gravity, water absorption, and flakiness index) for determining a better combination. The results showed that the combination (RCA/RAP) that best meets the NA aggregates specifications used for hot mix asphalt were RCA/RAP: 25/75 and 50/50. The results show the possibility of combining both wastes to obtain a coarse aggregate fraction with a high environmental benefit, by reducing the use of natural resources.