The accurate prediction of surface subsidence induced by coal mining is critical to safeguarding the environment and resources. However, the precision of current prediction models is often restricted by the lack of pertinent data or imprecise model parameters. To overcome these limitations, this study proposes an approach to predicting mine subsidence that leverages Interferometric Synthetic Aperture Radar (InSAR) technology and the long short-term memory network (LSTM). The proposed approach utilizes small baseline multiple-master high-coherent target (SBMHCT) interferometric synthetic aperture radar technology to monitor the mine surface and applies the long short-term memory (LSTM) algorithm to construct the prediction model. The Shigouyi coalfield in Ningxia Province, China was chosen as a study area, and time series ground subsidence data were obtained based on Sentinel-1A data from 9 March 2015 to 7 June 2016. To evaluate the proposed approach, the prediction accuracies of LSTM and Support Vector Regression (SVR) were compared. The results show that the proposed approach could accurately predict mine subsidence, with maximum absolute errors of less than 2 cm and maximum relative errors of less than 6%. The findings demonstrate that combining InSAR technology with the LSTM algorithm is an effective and robust approach for predicting mine subsidence.