In order to improve the accuracy of air quality information prediction, Logistic chaotic mapping strategy, refraction reverse learning strategy, adaptive weights, Levy flight strategy and Cauchy mutation strategy were introduced to improve the symbiotic organisms search (SOS) algorithm. The parameters of variational mode decomposition (VMD) algorithm and long short-term memory(LSTM) neural network model were optimized by the improved algorithm, and the ARIMAX-VMD-LSTM error correction air quality index combined prediction model optimized by the modified symbiotic organisms search (MSOS) algorithm was proposed. Firstly, recursive feature elimination (RFE) was used to filter the features. Secondly, autoregressive integrated moving average with exogenous input (ARIMAX) model was used to capture the linear relationship in air quality time series. Thirdly, VMD algorithm was used to decompose the nonlinear and complex ARIMAX error, and several modal components and a residual margin were obtained. LSTM model optimized by MSOS algorithm was used to predict the decomposed sub-sequences respectively, and the nonlinear relationship in ARIMAX error was captured. Finally, the error prediction result was obtained by superposition of each sub-sequence prediction result, and the ARIMAX prediction value was modified. The simulation results show that the combined model combining deep learning and statistical algorithm can further improve the prediction accuracy, and the variational mode decomposition can not only greatly reduce the nonlinear and complexity of the error sequence, but also improve the stability, and the error correction can further improve the prediction ability of the model. Compared with other models, the combined prediction model has the best evaluation indexes, higher prediction accuracy and generalization performance, and provides a new method for air quality prediction.