With the continuous decline of water resources due to population growth and rapid economic development, precipitation prediction plays an important role in the rational allocation of global water resources. To address the non-linearity and non-stationarity of monthly precipitation, a combined prediction method based on complementary ensemble empirical mode decomposition (CEEMD) and a modified long short-term memory (LSTM) neural network was proposed. Firstly, the CEEMD method was used to decompose the monthly precipitation series into a set of relatively stationary sub-sequence components, which can better reflect the local characteristics of the sequence and further understand the nonlinear dynamic characteristics of the sequence. Then, improved LSTM neural networks were employed to predict each sub-sequence. The proposed improvement method optimized the hyper-parameters of LSTM neural networks using particle swarm optimization algorithm, which avoided the randomness of artificial parameter selection. Finally, the predicted results of each component were superimposed to obtain the final prediction result. The proposed method was validated by taking the monthly precipitation data from 1961 to 2020 in Changde City, Hunan Province as an example. The results of the case study show that, compared with other traditional prediction methods, the proposed method can better reflect the trend of precipitation changes and has higher prediction accuracy.