• A hybrid method for short-term load forecasting, namely RF-MGF-RSM model, was established. • The paper constructed on multivariable response surface method to well solve the fluctuating problems of the peaks and valleys load data. • The proposed model shows stronger robustness and significantly greater forecasting accuracy for short-term loads. Accurate load forecasting is helpful for optimizing the use of power resources. To this end, this investigation proposes a hybrid model for short-term load forecasting, namely the RF-MGF-RSM model, that hybridizes random forest (RF) model and the mean generating function (MGF) model. A time variable, a random forest forecasting value, and a forecasting value by MGF are used as the input variables to in the modeling processes. The RF-MGF-RSM model uses its primary error as the response. The forecasted values of RF and MGF are the input variables to obtain the final forecast through the response surface method. Numerical experiments prove that the hybrid model has a significantly greater forecasting accuracy for short-term load than the original model that is based on selected forecasting accuracy indicators, especially with respect to peaks and valleys in greatly fluctuating data.