Short-term power demand forecasting plays an important role in the rational distribution of power utilization, reducing energy waste and enhancing the grid-connected operation of the power system. Using the single model of the seasonal auto regressive integrated moving average to forecast electricity demand will limit its prediction accuracy. In order to improve the prediction accuracy of the SARIMA model, the SARIMA-GS-SVR combined forecasting model is proposed in this study. The grid search algorithm is used to bring the residual predicted by SARIMA into the support vector regression model for parameter training, and the best parameters for optimization are brought into the SVR to predict the residuals. The obtained residual prediction results and the SARIMA prediction results are added together for comprehensive analysis. SARIMA, SVR, GS-SVR and SARIMA-GS-SVR forecasting models are established, and California’s historical electricity demand data is taken as an example to predict the 24-hour electricity demand in California on a certain day. In order to reflect the overall superiority of the model, the exponential smoothing method is selected as an irrelevant benchmark model for experimental comparison. The results show that compared with the SARIMA model, the prediction accuracy of the SARIMA-GS-SVR model is increased by 29.181 2%, and the three error index values of the SARIMA-GS-SVR model such as MAE, MAPE and RMSE are significantly lower than the other four models.