During high-intensity transportation on heavy-haul railways, rail stripping damage, abrasion, and other forms of damage that compromise driving safety can occur easily. Monitoring and predicting the condition of the rails are crucial steps to ensure the safe operation of the railway. However, current methods for detecting rail damage primarily rely on manual road inspections. These methods often suffer from issues such as strong subjectivity, challenges in quantifying the extent of damage, and difficulty in predicting the degradation trend of the damage. In response to the aforementioned issues, a novel approach was introduced to predict the stripping damage degradation trend of heavy-haul railway rails based on principal component analysis(PCA) and temporal convolutional networks with attention(TCN-Attention). Firstly, time domain and frequency domain features were extracted from the vibration signal associated with rail stripping damage. Subsequently, PCA was applied to reduce the dimensionality of the extracted high-dimensional features. Secondly, leveraging the distinctions in characteristics among time series samples, a degradation index for rail stripping damage was formulated to depict the degradation trend and address the challenge of measuring the damage state. The TCN network model, coupled with the Attention mechanism, was employed to focus on significant features and enhance the prediction accuracy of the model. Finally, the effectiveness of the proposed method was validated using vibration data collected throughout the entire life cycle of the rail, from normal to damaged to failure stages, obtained from a railway locomotive depot. Experimental results demonstrate that the proposed method accurately predicts rail stripping damage and loss of degradation trend.