The cut slope graben is affected by the lithology of strata, rainfall, and man-made excavation, which is a complex geotechnical system. Deformation of a cut slope changes irregularly with time, and, if too large, the deformation causes geological disasters such as landslides. Thus, it is crucial to establish an accurate slope deformation prediction model for control and safety. We used wavelet decomposition (WD) to process the time series of slope deformation to obtain an approximate series and detailed series. Then to predict each sub-series, we used the improved particle swarm optimization (IPSO) algorithm to optimize the number of neurons in the hidden layer, the learning rate, and the number of iterations of a long short-term memory (LSTM) neural network. The prediction results were summed to obtain the final prediction. The hybrid WD-IPSO-LSTM prediction model had a mean absolute error of 0.047, 0.067, and 0.094 at 1, 3, and 6 steps, respectively. These errors were 47.19%, 49.62%, and 57.47% lower than the LSTM-alone model errors. The hybrid WD-IPSO-LSTM prediction model had greater accuracy compared with a back propagation neural network, recurrent neural network, LSTM alone, PSO-LSTM, and IPSO-LSTM in 1-step, 3-step, and 6-step prediction. In addition, our hybrid model for prediction of slope deformation was more realistic and credible compared with other models.