Abstract: The prediction of air quality during the winter and spring seasons can be used for the public to make reasonable arrangements for travel and traffic management by relevant government departments. The main influencing factors of PM_2.5 concentration include atmospheric pollutants, precipitable water vapor (PWV), etc. To improve the accuracy of PM_2.5 concentration prediction, taking Beijing-Tianjin-Hebei region as an example, it was combined fast Fourier transform (FFT) and LSTM neural network methods, considered observation elements such as GNSS, ERA5 PWV, and atmospheric pollutants, and constructed the PM_2.5 concentration prediction model to predict the concentration of PM_2.5 in the next 24 hours. It was used GNSS PWV to correct the ERA5 PWV in the region and evaluated the accuracy. The public change period of air pollutants, ERA5 PWV and other observation elements are extracted by FFT, and the optimal public period is 78 hours; Select various factors with the best common cycle length as the model input, and the PM_2.5 concentration of the 24 hour sequence as the model output. Evaluate model accuracy through RMSE evaluation indicators. The research results are indicated that the accuracy of ERA5 PWV correction model based on GNSS is better than 2 mm in autumn and winter seasons. The prediction accuracy of the FFT-LSTM model is 10.22 μg/m³ in plain, 8.56 μg/m³ in mountainous, and 9.02 μg/m³ in plateau regions, while the predicted time limit of 24 hours. It can effectively predict the PM_2.5 concentration in the next 24 hours. This model can provide reference for relevant departments in air pollution control.