Structural health monitoring is of great significance to prevent structural disasters. However, the sensors in the structure monitoring system inevitably produce a large number of abnormal data. To ensure the integrity and practicability of monitoring data, it is necessary to recover abnormal monitoring data. Most existing data recovery methods use the correlation between variables and spatial correlation, rather than fully mine the temporal correlation of data. An abnormal data recovery framework based on a gated recurrent unit (GRU) neural network and temporal correlation is proposed in this study. The abnormal data recovery framework can be independent of other sensors. The input and output configurations of the GRU model are optimized. Bidirectional prediction including forward and backward prediction information is used to improve the prediction accuracy of the model. The framework is demonstrated using monitoring data of beam-end displacement and pylon tower tilt collected from Waitan Bridge in Ningbo, China. The results show that the framework has high accuracy in abnormal data recovery. After data recovery, the linear relationship between structural response and temperature is significantly improved.