In view of the problems of low prediction accuracy of the initial moment after the change point of the two-stage residual life prediction model, a remaining useful life prediction algorithm based on the data processing at the change point is proposed. Firstly, the Wiener process was used to construct the degradation model and the expectation maximization algorithm with Bayesian method was used to realize parameter updating. The degraded data were identified at the change point, and part of the degraded data before the change point were determined to be used for the life prediction at the initial moment after the change point to reduce prediction error. Finally, the algorithm was validated using simulation data and NASA test data, respectively. The results show that the prediction accuracy of the proposed algorithm is further improved. According to the prediction results of NASA test data, compared with the single-stage life prediction model and two-stage life prediction model, the root mean square error is reduced by 10.76 and 1.78 respectively, which is of great significance for the prediction of the remaining life of the product.