A weldable Al–Mg–Zn–Sc alloy was produced using vacuum induction melting and an argon-protected casting method to achieve high strength and ductility, and the effects of heat treatment on the microstructure evolution and mechanical properties of Al–Mg–Zn–Sc alloys were comparatively investigated. The results reveal that fine equiaxed grains with an average grain size of 40 μm in an as-cast Al–Mg–Zn–Sc alloy change little after heat treatments, bringing about a grain-boundary strengthening of 46.1 MPa. The coarse T-Mg32(Al, Zn)49 phases at grain boundaries are completely dissolved into the matrix through solid-solution treatment, and T-Mg32(Al, Zn)49 with diameters ranging from 10 to 25 nm and Al3Sc with diameters ranging from 5 to 20 nm gradually precipitate during the artificial aging process. The Mg solid solubility is 4.67% in the as-cast Al–Mg–Zn–Sc alloy, and it increased to 5.33% after solid-solution treatment and dramatically decreased to 4.15% after post-aging treatment. The contributions of solid-solution strengthening to as-cast, post-solid-solution and post-aging Al–Mg–Zn–Sc alloys are 78.2 MPa, 85.4 MPa and 72.3 MPa, respectively. The precipitation strengthening of the post-aging alloy is 49.7 MPa, which is an increase of 21% in comparison to that of both as-cast and post-solid-solution alloys. The alloy achieves an optimal tensile strength of 355.3 MPa, yield strength of 175 MPa and elongation of 22% after undergoing solid-solution treatment.