Accurate prediction of regional precipitation plays an important role in preventing natural disasters and protection of human life and property. In this study, non-linear monthly precipitation data are decomposed into multiple subsignal intrinsic mode functions (IMFs) with different central frequencies based on variational modal decomposition (VMD) to mine multi-scale features. Then, a hybrid model built with long short-term memory (LSTM) and the autoregressive integrated moving average model (ARIMA) is used to predict the residuals and IMFs. The hyperparameters of LSTM are optimized using the modified slime mould algorithm (MSMA) based on the adaptive strategy and spiral search. This study also utilizes the model to predict precipitation in two regions. The empirical results show the VMD-MSMA-LSTM-ARIMA model performs better and its prediction is more accurate compared with others. The deep learning model established in this study can provide some reference for the accurate prediction of future precipitation in different regions.