Recently, nanomaterials have attracted attention in the field of pavement construction as modifiers to endure heavy loads and climate changes. In this study, conventional asphalt (bitumen) of penetration grade AC (60/70) was modified with graphene platelets (GnPs) at three different contents: 0.5%, 1.0%, and 1.5% by weight of asphalt content. Kinematic viscosity, softening point, penetration, and dynamic shear rheology tests were performed to evaluate the mechanical properties of modified binder. The results showed that adding GnPs improves the mechanical properties of asphalt binder; the kinematic viscosities, softening points, and rutting parameters increased but penetrations decreased with the contents of GnPs. Hot mix asphalt specimens with GnPs-modified asphalt were prepared and characterized with Marshall tests, thermal stress restrained specimen tests (TSRST), wheel tracking tests, and indirect tensile tests. Similar to the results of asphalt binder, the mechanical properties of asphalt mixture were improved by GnPs. Marshall stability increased by 21% and flow decreased by 24% with accepted value of 2.8 mm in penetration when the mixture was modified with 1.0 wt% of GnPs. At the same GnPs content, modified asphalt mixture led to lower failure temperature by 2 °C in comparison with unmodified asphalt mixture and the cryogenic failure stress was improved by 12%. The wheel tracking tests showed that GnPs-modified asphalt mixture has outstanding deformation resistance in comparison with unmodified asphalt mixtures: after 5000 cycles, 1.0 wt% of GnPs reduced the rut depth of asphalt mixture by 60%—the rut depth of unmodified asphalt mixture was 6.9 mm compared to 2.75 mm for modified asphalt mixture. After 10,000 cycles, the modified asphalt mixture showed rut depth of 3.24 mm in comparison with 8.12 mm in case of unmodified asphalt mixture. Addition of GnPs into asphalt mixture significantly improved the indirect tensile strength: 1.0 wt% of GnPs increased the indirect tensile strength of unmodified asphalt mixture from 0.79 to 1.1 MPa recording ~40% increment. The results of this study can confirm that graphene platelets enhance the mechanical properties of asphalt mixture and its performance.