Bridge monitoring data prediction plays a crucial role in maintaining the serviceability and safety of bridges. To assess the performance of bridge structures in advance, an accurate and robust prediction model for measurement data prediction is needed. In this context, this paper presents a novel hybrid prediction model called IGWO-VMD-IGWO-LSTM, which aims to improve the accuracy and generalization ability of bridge monitoring data prediction. First, the proposed model incorporates variational mode decomposition (VMD) and an improved gray wolf optimization (IGWO) algorithm to decompose the measured data into several intrinsic mode functions (IMFs) to capture the signal’s features comprehensively. Then, long short-term memory (LSTM) models are established individually for each IMF, with hyperparameters optimization using the IGWO algorithm. Finally, the integrated reconstructed subsequences yield the prediction results of the proposed IGWO-VMD-IGWO-LSTM model. Thus, the proposed framework avoids exploring the complex internal mechanism of bridge behavior evolution. The measurement data collected from a real bridge demonstrates the feasibility of the proposed prediction method, and different deep learning models are used for comparison. The results demonstrate a significant improvement in prediction performance comparison with the other concerned models, highlighting the strong generalization ability and robustness of the proposed IGWO-VMD-IGWO-LSTM model.