Objective To explore PM_2.5 concentration modeling and prediction based on the monthly average concentrations of PM_2.5 in Shanghai since 2015, and to provide new ideas about PM_2.5 prediction methods. Methods The seasonal factors were introduced into the Grey Model (GM). GM(1,1) model modified with seasonal factors was established and compared with seasonal autoregressive integrated moving average model (ARIMA) model. The data of 2015-2021 was used for modeling and prediction, and the data from January to October in 2022 was used as a validation set to evaluate the prediction effectiveness. The monthly average PM_2.5 concentrations in Shanghai from November to December in 2022 were predicted. Results Seasonal ARIMA model showed RMSE=4.02 and MAPE=15.50% in the validation set, while GM(1,1) model modified with seasonal factors showed RMSE=3.30 and MAPE=11.59%. GM(1,1) model modified with seasonal factors predicted the monthly average PM_2.5 concentrations in Shanghai from November to December in 2022 to be 24.99 and 34.83μg/m3, respectively. Conclusion The prediction effect of GM(1,1) model modified with seasonal factors has better predictive performance than seasonal ARIMA model. The grey prediction model modified with seasonal factors can be considered when predicting seasonal time series such as the concentration of PM_2.5.