In the absence of enough run-to-failure data, step-stress accelerated degradation testing (SSADT) is often an attractive alternative way to evaluate the reliability of a product, with the advantage of requiring small sample size and short test time. However, the development of a statistical SSADT model for reliability assessment should take into account different sources of variability in the degradation process that generate uncertainty: 1) temporal variability determining the inherent variability of degradation process over time; 2) unit-to-unit variability in three aspects: degradation rates, initial degradation values, time-points of elevating stress levels; and 3) measurement errors in both covariates and degradation performance. As a contribution towards this aim, a new nonlinear Wiener-process-based SSADT model considering simultaneously nonlinearity and three sources of variability is proposed. Using the proposed SSADT model, the lifetime law of the tested product under normal conditions is derived based on the concept of first hitting time (FHT) of a predetermined failure threshold. Following an approach based on genetic algorithms (GA), a modified simulation and extrapolation method, called GA-SIMEX, is also developed for the model parameter estimation. Finally, a simulation study of fatigue crack length growth is presented to illustrate the implementation of the proposed SSADT model.