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Missing data, especially a block of missing data, inevitably occur in structural health monitoring systems. Because of their severe negative effects, many methods that use measured data to infer missing data have been proposed in previous research to solve the problem. However, capturing complex correlations from raw measured signal data remains a challenge. In this study, empirical mode decomposition is combined with a long short-term memory deep learning network for the recovery of the measured signal data. The proposed hybrid method converts the missing data imputation task as a time series prediction task, which is then solved by a “divide and conquer” strategy. The core concept of this strategy is the prediction of the subsequences of the raw measured signal data, which are decomposed by empirical mode decomposition rather than directly predicted, as the decomposition can assist in the modeling of the irregular periodic changes of the measured signal data. In addition, the long short-term memory network in the hybrid model can remember more long-range correlations of subsequences than can the traditional artificial neural network. Three widely used prediction models, namely, the autoregressive integrated moving average, support vector regression, and artificial neural network models, are also implemented as benchmark models. Raw acceleration data collected from a cable-stayed bridge are used to evaluate the performance of the proposed method for missing measured signal data imputation. The recovery results of the measured signal data demonstrate that the proposed hybrid method exhibits excellent performance from two perspectives. First, the decomposition by empirical mode decomposition can improve the accuracy of the core long short-term memory prediction model. Second, the long short-term memory model outperforms other benchmark models because it can fit more microscopic changes of measured values. The experiments conducted in this study also suggest that the change patterns of raw measured signal data are complex, and it is therefore important to extract the features before modeling.