Accurate prediction of the remaining useful life (RUL) of bearings is essential for the health management of mechanical equipment. When facing unknown target bearings, due to significant data distribution discrepancy between training and testing set, the existing leaning-based RUL models do not has Out-of-Distribution generalization performance. To address the problem, this paper proposes a causal stable learning-based single-source domain generalization RUL prediction method for unknown bearings, including data preprocessing, stable encoder, and RUL prediction modules. First, we use time domain, frequency domain, and time-frequency domain metrics to extract physical features from the original vibration data of the bearing, and adds noise into the features to improve the model's generalization capability. Further we design a causal stable learning encoder to extract causal feature representations from the physical features of single source domain/training bearing, for the purpose of constructing an effective health indicator that can remove irrelevant features and accurately express the degradation trend of bearings. Finally, a gated recurrent units(GRU)-based RUL prediction module is employed to predict the RUL of different bearings. Experimental results show that the proposed method performs optimal performance for target bearings under different working conditions.