In the Loess Plateau of China, loess creep characteristics with time effects are crucial factors influencing slope stability. Especially under extreme climates, after being subjected to repeated dry-wet cycles (DWC), the creep deformation of loess is more intense, leading to large-scale and frequent disasters such as landslides. In this study, a series of direct shear creep tests was performed on the loess samples after dry-wet cycles to understand the effect of DWC on loess creep characteristics profoundly. The results show that the loess is more vulnerable to creep failure after being subjected to dry-wet cycles; the greater the normal stress of the loess, the more pronounced the effect of dry-wet cycles, and the more significant the creep deformation under shear stress. Moreover, the long-term shear strength of loess decreases exponentially as the DWC increases. Based on the Burgers model, a new nonlinear viscoelastic-plastic rheological model (NVPM model) is proposed, which can accurately describe the entire loess creep curve under the effect of dry-wet cycles, especially for the accelerated creep stage that the Burgers model cannot fit. Based on the shear creep test results, the creep parameters obtained from the NVPM model were applied to a numerical simulation of a typical loess slope. The results reveal that the NVPM model is capable of reasonably explaining the stability deformation law of a loess slope under the coupling effect of DWC and creep, and the causes of loess landslides. The research results can provide a theoretical reference for the long-term stability analysis and prediction of loess slopes.