A method for preparing asphalt modified with a polymer nanocomposite additive comprising styrene-butadiene-styrene and multi-walled carbon nanotubes SBS/MWCNT nanocomposite, characterized in that it comprises the following steps: preparing a polymer nanocomposite additive, wherein the styrene-butadiene-styrene polymer is in the form of pellets or crumbs, and the multi-walled carbon nanotubes (MWCNT) have a diameter between 5-50 nm and a length between 1-30 μm and are functionalized with hydroxyl groups, with carboxylic acid groups, with amino groups, with phenol, or with alkyl groups, by a) dispersing multi-walled carbon nanotubes in a solvent by ultrasound and/or mechanical stirring, wherein the solvent is selected between xylenes, toluene, acetone, tetrahydrofuran, chloroform, cyclohexane, ethanol, methanol, propanol, dimethylformamide, or a combination thereof, and wherein the solvent/polymer weight ratio between 1 and 20 and with a solvent/MWCNT weight ratio between 10 and 10000; b) dissolving a styrene-butadiene-styrene polymer in a solvent by mechanical stirring; c) mixing the multi-walled carbon nanotubes dispersion of step (a) with the styrene-butadiene-styrene solution of step (b) by ultrasound and/or mechanical stirring; and d) evaporating the solvent of the mixed obtained in step (c); and mixing the dried polymer nanocomposite additive obtained in step (d) with the asphalt base by mechanical stirring. preparing a polymer nanocomposite additive, wherein the styrene-butadiene-styrene polymer is in the form of pellets or crumbs, and the multi-walled carbon nanotubes (MWCNT) have a diameter between 5-50 nm and a length between 1-30 μm and are functionalized with hydroxyl groups, with carboxylic acid groups, with amino groups, with phenol, or with alkyl groups, by a) dispersing multi-walled carbon nanotubes in a solvent by ultrasound and/or mechanical stirring, wherein the solvent is selected between xylenes, toluene, acetone, tetrahydrofuran, chloroform, cyclohexane, ethanol, methanol, propanol, dimethylformamide, or a combination thereof, and wherein the solvent/polymer weight ratio between 1 and 20 and with a solvent/MWCNT weight ratio between 10 and 10000; b) dissolving a styrene-butadiene-styrene polymer in a solvent by mechanical stirring; c) mixing the multi-walled carbon nanotubes dispersion of step (a) with the styrene-butadiene-styrene solution of step (b) by ultrasound and/or mechanical stirring; and d) evaporating the solvent of the mixed obtained in step (c); and a) dispersing multi-walled carbon nanotubes in a solvent by ultrasound and/or mechanical stirring, wherein the solvent is selected between xylenes, toluene, acetone, tetrahydrofuran, chloroform, cyclohexane, ethanol, methanol, propanol, dimethylformamide, or a combination thereof, and wherein the solvent/polymer weight ratio between 1 and 20 and with a solvent/MWCNT weight ratio between 10 and 10000; b) dissolving a styrene-butadiene-styrene polymer in a solvent by mechanical stirring; c) mixing the multi-walled carbon nanotubes dispersion of step (a) with the styrene-butadiene-styrene solution of step (b) by ultrasound and/or mechanical stirring; and d) evaporating the solvent of the mixed obtained in step (c); and mixing the dried polymer nanocomposite additive obtained in step (d) with the asphalt base by mechanical stirring.