It is crucial to predict landslide displacement accurately for establishing a reliable early warning system. Such a requirement is more urgent for landslides in the reservoir area. The main reason is that an inaccurate prediction can lead to riverine disasters and secondary surge disasters. Machine learning (ML) methods have been developed and commonly applied in landslide displacement prediction because of their powerful nonlinear processing ability. Recently, deep ML methods have become popular, as they can deal with more complicated problems than conventional ML methods. However, it is usually not easy to obtain a well-trained deep ML model, as many hyperparameters need to be trained. In this paper, a deep ML method—the gated recurrent unit (GRU)—with the advantages of a powerful prediction ability and fewer hyperparameters, was applied to forecast landslide displacement in the dam reservoir. The accumulated displacement was firstly decomposed into a trend term, a periodic term, and a stochastic term by complementary ensemble empirical mode decomposition (CEEMD). A univariate GRU model and a multivariable GRU model were employed to forecast trend and stochastic displacements, respectively. A multivariable GRU model was applied to predict periodic displacement, and another two popular ML methods—long short-term memory neural networks (LSTM) and random forest (RF)—were used for comparison. Precipitation, reservoir level, and previous displacement were considered to be candidate-triggering factors for inputs of the models. The Baijiabao landslide, located in the Three Gorges Reservoir Area (TGRA), was taken as a case study to test the prediction ability of the model. The results demonstrated that the GRU algorithm provided the most encouraging results. Such a satisfactory prediction accuracy of the GRU algorithm depends on its ability to fully use the historical information while having fewer hyperparameters to train. It is concluded that the proposed model can be a valuable tool for predicting the displacements of landslides in the TGRA and other dam reservoirs.