Bridge Health Monitoring (BHM) systems generate nonstationary time-series data that pose challenges for accurate structural state prediction. This study proposes a novel neural network-based method for predicting bridge states, the Temporal Multi-Scale Convolutional Neural Network (T-MSCNN) to enhance the prediction of dynamic strain parameters, which directly reflect structural stress states. The T-MSCNN integrates multi-scale convolutional layers for local feature extraction and gated recurrent units (GRUs), by using the Convolutional Neural Network (CNN) model and the Gated Recurrent Unit (GRU) model to address the intricacies of the nonstationary BHM data. Validated with real strain data from the Qijiang River Bridge in China, the model demonstrated superior performance over traditional models (HA, ARIMA, SVR) and standalone deep learning models (CNN, GRU), achieving reductions in prediction error by Root Mean Square Error (RMSE) method—up to 77.7%, compared to the ARIMA model and consistently improving even over the strong GRU baseline. The perturbation analysis confirms its robustness under noise interference. The T-MSCNN provides a reliable data-driven framework for structural health diagnostics, with potential applicability to other fields involving nonlinear spatiotemporal data analysis.