Accurate and effective PM2.5 concentration prediction has important implications for public health and the ecological environment. To provide more accurate early warnings for haze prevention, urban planning, and people's travel planning, this paper proposes a new combined PM2.5 concentration prediction model. Firstly, the original sequence is decomposed by complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), followed by decomposition and reconstruction of the data by adaptive variational mode decomposition (AVMD) and sample entropy (SE), and then the reconstructed subseries are predicted by long and short-term memory networks (LSTM). The empirical analysis was carried out with three datasets from Beijing, Tianjin, and Baoding, and the following conclusions can be drawn: (1) The validity and robustness of the proposed model were verified, with R-2 (0.982), RMSE (2.792), and MAPE (9.088%) being optimal in all comparison experiments. (2) The incorporation of secondary decomposition and pattern reorganization algorithms can effectively handle data with high volatility and non-linearity. (3) Compared with traditional machine learning models, the long and short-term memory network is more suitable for time series prediction. The model provides a novel and effective PM2.5 concentration prediction tool for the government and the public.