Nanocrystalline (NC) structure can lead to the considerable strengthening of metals and alloys. Obtaining appropriate comprehensive mechanical properties is always the goal of metallic materials. Here, a nanostructured Al-Zn-Mg-Cu-Zr-Sc alloy was successfully processed by high-pressure torsion (HPT) followed by natural aging. The microstructures and mechanical properties of the naturally aged HPT alloy were analyzed. The results show that the naturally aged HPT alloy primarily consists of nanoscale grains (~98.8 nm), nano-sized precipitates (20–28 nm in size), and dislocations (1.16 × 1015m−2), and exhibits a high tensile strength of 851 ± 6 MPa and appropriate elongation of 6.8 ± 0.2%. In addition, the multiple strengthening modes that were activated and contributed to the yield strength of the alloy were evaluated according to grain refinement strengthening, precipitation strengthening, and dislocation strengthening, and it is shown that grain refinement strengthening and precipitation strengthening are the main strengthening mechanisms. The results of this study provide an effective pathway for achieving the optimal strength–ductility match of materials and guiding the subsequent annealing treatment.