Research on landslide displacement prediction based on interferometric synthetic aperture radar (InSAR) deformation data involves two main issues. First, InSAR can provide only one-dimensional deformation data along the satellite’s line of sight (LOS), which cannot truly reflect the deformation of the landslide body in the downward direction along the slope. Second, the use of a single prediction model does not adequately account for both long-term and local changes in landslide displacement, affecting the accuracy of the predictions. To address this, in this study, Long Short-Term Memory networks (LSTM) and temporal convolutional network (TCN) models are combined to construct a method (LSTM-TCN) of landslide displacement prediction. This method can consider the long-term and localized changes in landslide displacement. The method is first based on InSAR technology to obtain surface deformation. The deformation of the landslide is subsequently computed in the downward direction along the slope to obtain the landslide displacement time series data. Next, the LSTM-TCN is used for landslide displacement prediction. Finally, the mean absolute error (MAE), root mean square error (RMSE) and coefficient of determination (R2) are used to evaluate the performance of the model. The experiment is conducted on the Xiao Andong landslide in Anshi village, Fengqing County, Lincang City, Yunnan Province, China. The LSTM-TCN model achieves an R2 of 0.75, an RMSE of 0.43 cm, and an MAE of 0.36 cm. Compared with the individual LSTM and TCN models, the LSTM-TCN model exhibits the highest prediction accuracy and the smallest prediction error, which is closer to the true result that in the other models. These results demonstrate that the combined LSTM-TCN model effectively captures the complex features and long-term trends in landslide displacement data, significantly enhancing the accuracy of predictions.