Abstract: The invention relates to a method for modifying an asphalt binder using, as an additive, a nanocomposite of: functionalized multi-walled carbon nanotubes dispersed in a styrene-butadiene-styrene polymer matrix (SBS/MMWCNT). The asphalt modified with the SBS/MMWCNT nanocomposite has substantially improved mechanical resistance to deformations and to loads at high temperatures, such that the life of the flexible paving is improved. The asphalt mixtures produced with this novel modified asphalt binder have considerably less rutting, are classified as high-modulus asphalt mixtures when produced from asphalt of medium (60/70) or greater hardness, and are not sensitive to moisture effects.