Three different percentages of carbon nanotubes (CNTs) (0.1%, 0.5%, and 1% by mass of asphalt cement) were used to modify conventional asphalt cement (60/70) in this study. Mechanical properties of modified asphalt cement and mixture were evaluated. Penetration grade, kinematic viscosity, softening point and dynamic shear rheometer test were measured to evaluate physical properties of modified asphalt cement. The results exhibited that modifying asphalt cement with CNTs decreased its penetration and increased its kinematic viscosity and softening point. Rutting parameter increased with CNTs at the given temperature for both unaged and RTFOT-aged samples. Marshall stability tests, low temperature cracking tests, indirect tensile tests and wheel tracking tests were conducted to assess the mechanical performance of modified hot asphalt mixture. The Marshall stability increased with CNTs but no significant difference at 0.5 and 1.0 wt%, while Marshall flow decreased with CNTs. The results of wheel tracking test showed that rut depth decreased by 45% upon adding 0.5% CNTs by weight of asphalt cement; also, this percentage of CNTs endowed improvement in low temperature cracking and indirect tensile strength of the asphalt concrete. This study underlines that adding CNTs into asphalt cement enhances the performance of asphalt concrete pavement in both hot and cold weather, which in turn prolongs the pavement’s service life and saves maintenance expenses.