A key component of disaster management and infrastructure organization is predicting cumulative deformations caused by landslides. One of the critical points in predicting deformation is to consider the spatio-temporal relationships and interdependencies between the features, such as geological, geomorphological, and geospatial factors (predisposing factors). Using algorithms that create temporal and spatial connections is suggested in this study to address this important point. This study proposes a modified graph convolutional network (GCN) that incorporates a long and short-term memory (LSTM) network (GCN-LSTM) and applies it to the Moio della Civitella landslides (southern Italy) for predicting cumulative deformation. In our proposed deep learning algorithms (DLAs), two types of data are considered, the first is geological, geomorphological, and geospatial information, and the second is cumulative deformations obtained by permanent scatterer interferometry (PSI), with the first investigated as features and the second as labels and goals. This approach is divided into two processing strategies where: (a) Firstly, extracting the spatial interdependency between paired data points using the GCN regression model applied to velocity obtained by PSI and data depicting controlling predisposing factors; (b) secondly, the application of the GCN-LSTM model to predict cumulative landslide deformation (labels of DLAs) based on the correlation distance obtained through the first strategy and determination of spatio-temporal dependency. A comparative assessment of model performance illustrates that GCN-LSTM is superior and outperforms four different DLAs, including recurrent neural networks (RNNs), gated recurrent units (GRU), LSTM, and GCN-GRU. The absolute error between the real and predicted deformation is applied for validation, and in 92% of the data points, this error is lower than 4 mm.