Sulfate attack progressively degrades concrete stiffness and accelerates long-term creep. Existing creep models mainly address sound concrete and do not represent the spatial gradient of corrosion products within the interfacial transition zone (ITZ). This study develops a multi-scale homogenization framework, coupling phase evolution, layered ITZ corrosion, and viscoelastic creep. The ITZ is discretized into sub-layers, with corrosion degree decaying exponentially from the aggregate surface, and the decay coefficient is calibrated from measured sulfate concentration profiles. Phase volume fractions are updated with corrosion degree, and the effective elastic modulus is obtained using Mori–Tanaka homogenization. Creep compliance is then predicted with a Burgers model, whose parameters depend on the homogenized modulus and corrosion product content. The framework reproduces the non-monotonic evolution of elastic modulus under different sulfate concentrations, with a mean absolute percentage error below 10%. At a corrosion degree of 0.3, the predicted relative creep increment reaches approximately 11% at 365 days. The effects of temperature, loading age, and wet–dry cycles are also quantified. Sensitivity analyses identify the long-term creep modulus and corrosion product coefficient as the dominant parameters. The model provides a physically grounded tool for assessing the long-term deformation of sulfate-attacked concrete.