Two-stage prediction methods based on Wiener processes are widely used to describe the degradation process of components. However, a single type of drift function cannot accurately track the two-stage degradation path of the component for long-range and identify the change point between stages, which decreased prediction accuracy of models. Therefore, this paper proposes a new two-stage remaining useful life prediction model, which uses the degradation angle (DA) to solve the above problems. Firstly, the idea of DA is proposed to accurately identify the change point between slow degradation stage (SDS) and accelerated degradation stage (ADS) so that different drift functions match different degradation states of the component. Secondly, according to the definition of the DA and the first hitting time, this paper respectively obtains the probability density function of the SDS and the ADS to estimate the component degradation state. Then, a three-step method is proposed to estimate the unknown parameters in the model and update them by Bayesian method. Finally, the effectiveness of the proposed method is verified by bearing accelerated degradation experiment and XJTU-SY Bearing Datasets.