Climate change is increasingly affecting the global water cycle. Developing high-quality climate-runoff relationship models can help assess its impact on surface natural runoff, thereby enhancing resilience to water resource risks. This study extends the applicability paradigm of self-attention mechanisms to non-sequential hydrological modeling by developing a Self-Attention Artificial Neural Network (SAANN), which quantifies climate change impacts on China's natural runoff. The model was trained with climate, underlying surface, and natural runoff data from China (2000-2018), utilizing Bayesian optimization for hyperparameter tuning. Compared to the ANN, SAANN's mean square error (MSE) in the test set is reduced by 26.9 %, demonstrating its superior prediction performance. SAANN visualizes the attention relationships between input variables in the model's attention layer, highlighting key correlations similar to physical model principles. This improves both model interpretability and output reliability. Based on the methodology developed above, the study predicts natural runoff in China for the near-term (2041-2050), mid-term (2061-2070), and long-term (2091-2100) under two emission scenarios (SSP245 and SSP585), and examines the driving factors. The results show that natural runoff in China is expected to increase under various future scenarios. Notably, the increase rate under the SSP585 scenario is significantly higher than that under SSP245. The autumn increase is particularly pronounced compared to other seasons, and the northern basin generally experiences a higher increase rate than the southern basin. These changes may pose new adaptive challenges for agricultural production and water conservancy in China.