The decision-making of power generation enterprises, power supply enterprises, and power consumers can be affected by forecasting the price of electricity. There are many irrelevant samples and features in big data, which often lead to low forecasting accuracy and high time-cost. Therefore, this paper proposes a forecasting framework based on big data processing, which selects a small quantity of data to achieve accurate forecasting while reducing the time-cost. First, the sample selection based on grey correlation analysis (GCA) is established to eliminate useless samples from the periodicity. Second, the feature selection based on GCA is established considering the feature classification and the temporal correlation features to further eliminate useless features. Third, principal component analysis is applied to reduce the noise among the data. Then, combined with a differential evolution algorithm (DE), a support-vector machine (SVM) is applied to forecast the price. Finally, the proposed framework is applied to the New England electricity market to forecast the short-term electricity price. The results show that, compared with DE-SVM without data processing, the forecasting accuracy is improved from 81.68% to 91.44%, and the time-cost is decreased from 35,074 s to 1,809 s which shows that the proposed method and model can provide a valuable tool for data processing and forecasting.