The remaining useful life prediction of rolling bearing holds significant importance in enhancing the operational reliability and reducing maintenance costs of the entire rotating machinery system. Deep learning techniques have shown promise in remaining useful life (RUL) prediction by leveraging their powerful representation learning capabilities. However, existing deep learning-based approaches still suffer from limitations such as reliance on hand-crafted features and lack of interpretability. Therefore, we propose an improved physics-informed neural networks (PINNs) based on deep separable convolutional network (DSCN) and attention mechanism for the RUL estimation of rolling bearings. Specifically, a deep separable convolutional network is introduced for feature extraction, which directly utilizes multisensor data as inputs and employs separable convolutional building blocks to automatically learn high-level representations. The features are then mapped to RUL using a self-attention mechanism-based physics-informed neural network. The hybrid prediction framework called DSCN-AttnPINN has demonstrated superior performance on the XJTU-SY dataset. The results of the experiments reveal that the DSCNAttnPINN can accurately predict RUL and outperforms certain current data-driven prognostics methods.