Aiming at the stochastic degradation device with performance degradation trend in the Step-Stress Accelerated Degradation Test (SSADT), a nonlinear Wiener process is used to establish a step-accelerated degradation model consistent with the degradation characteristics of the device. The Maximum Likelihood Estimation (MLE) algorithm is used to obtain the estimates of prior parameters. The current monitoring data of the target device is used to update the posterior distribution of random coefficients based on Bayesian method. The Remaining Useful Lifetime (RUL) distribution of the device considering the uncertainty of random coefficient estimation is derived by using the full probability formula. The correctness and superiority of the proposed method are verified by an example.