Owing to the pavement cracking of heightening and thickening levees (HTL) caused by differential settlement, it is necessary to study the settlement prediction and differential settlement criterion for HTLs. In this study, an HTL was taken as the study object. First, leveling observation and layered settlement observation were adopted, and a generalized settlement prediction model (GSPM) that can describe both S-shaped and hyperbolic settlement–time curves was proposed. The physical meanings of GSPM parameters were analyzed. Moreover, the effectiveness of the GSPM was verified using field monitoring data. Second, finite element analysis based on a viscoelastic constitutive model was used to reveal the quantitative relationship between the differential settlement and horizontal stress of the pavement. On this basis, the differential settlement criterion was obtained. The results showed that the GSPM can unify the logistic model and hyperbolic model by introducing two morphological change parameters. In addition, the GSPM can be more widely used, more accurate, and more stable than the traditional logistic model and hyperbolic model. When an asphalt concrete pavement (whose ultimate tensile stress is 0.12 MPa) is used, the corresponding differential settlement criterion is approximately 4.3 cm. The research results can provide a reference for reasonable differential settlement control for HTLs in order to prevent pavement cracking.