In long-term monitoring processes, the structural health monitoring(SHM) system often encounters data incompleteness due to various factors, including sensor malfunctions, power interruptions, and network transmission issues. To address this challenge, this study proposes a missing data reconstruction method for structural monitoring based on ensemble empirical mode decomposition(EEMD) and bidirectional long short-term memory(BiLSTM) networks, leveraging their advantages in time-series processing. The proposed approach utilizes EEMD to adaptively decompose the monitoring time-series data into a set of intrinsic mode functions (IMFs), each representing different time scales. This decomposition effectively transforms the nonlinear and non-stationary time-series signals into stationary components. The IMFs are then input into a BiLSTM network for missing data reconstruction, enhancing the prediction accuracy of the BiLSTM model. Analysis is conducted on a six-story scaled structural model and a benchmark finite element simulation model. Experimental results demonstrate that, compared to the mainstream methods such as EEMD-LSTM, BiLSTM, and LSTM, the proposed EEMD-BiLSTM approach achieves the highest prediction accuracy. In cases of 5%, 10% and 15% missing data, the R2 value remains above 0.8. Therefore, the use of the EEMD method for preprocessing non-stationary structural acceleration response data significantly improves the prediction accuracy of BiLSTM, providing a more adaptive solution to the problem of missing data in structural monitoring.