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Aiming at solving the problems of small fault data samples and insufficient remaining useful life (RUL) prediction accuracy of nuclear power machinery, a method based on an exponential degradation model is proposed to predict the RUL of equipment after the failure warning system alarm. After data preprocessing, time-domain feature extraction, selection, and dimensionality reduction fusion of multiple degradation variables, the exponential degradation model is constructed based on the Bayesian process, and prior information is used. As an application, the RUL of a nuclear power turbine was calculated based on actual monitoring data, the α−λ precision curve was used to evaluate the prediction effect, and the RUL prediction results verified the effectiveness of the proposed method.