In order to effectively predict the air quality indicators of heavily polluted days with small sample size and discontinuous time series, The data grouping GM(1,1) model with fractional order accumulation (DGFGM(1,1)) was used to predict AQI and the daily concentrations of PM_2.5, PM₁₀, NO₂ for December 28, 29 and 30 in Handan. The MAPE of the AQI, PM_2.5, PM₁₀ and NO₂ predicted by DGFGM(1,1) model were 2.89%, 3.28%, 3.83% and 3.23%, respectively, indicating that this model has a high prediction accuracy. The prediction results demonstrate that under the current governance measures, the occurrence of heavily polluted days is still inevitable, and the concentration of some air quality indicators will increase rather than decrease. Except for the daily concentrations of NO₂ on December 30 during 2018 to 2019, the concentrations of all air quality indicators exceeded the grade II standard of Chinese Ambient Air Quality at other times. Local departments should pay attention to the prevention and treatment of extremely heavy pollution days, so as to comprehensively improve the quality of atmospheric environment.