The accurate forecasting of daily natural gas load is pivotal to the reasonable supply and dispatch of energy in the city. This study proposes a multistage hybrid model based on Fuzzy Coding of Genetic Algorithms (FCGA) and the improved LSTM-BPNN residual correction model since gas load data is periodic but random and the single-stage and single-forecasting model has a limited role. In the first stage, the gas load is forecasted by the LSTM model to calculate its residual value. In the second stage, the residual value is predicted by the BPNN model, and then the learning rate of the LSTM-BPNN residual model is automatically adjusted with the Adam algorithm regarding the adaptive learning rate to accelerate fitting. Afterward, the initial weights and thresholds of the BPNN are optimized by the fuzzy coding of genetic algorithms to find the global optimal solution. Finally, the sum of the forecasting values in the two stages is taken as the final gas load. Comparative experiments prove that the model in this study ensures higher prediction accuracy than the single model and the original two-stage forecasting model.