This article introduces a new hybrid technique for predicting solar activity. The proposed hybrid technique consists of four phases. The first phase is feature selection, where the most relevant features (variables) are selected based on an artificial bee colony using a neighborhood rough set as the fitness function. The second phase employs the training support vector regression (SVR) using a part of the solar activity data set based on the selected features. Sequential minimal optimization is carried out to determine the optimal parameters of SVR. The third phase tests the regression model based on the second part of the data set. The fourth phase is the process of predicting solar activity. According to the prediction system, the maximum amplitude of cycle 25 is 80 ± 12, and it will occur in 2026. The solution quality is assessed by using three indices called average absolute percent relative error (AAPRE), root-mean-square error (RMSE), and coefficient of determination. These indices prove the high quality of the forecast sunspot number value and the actual ones. In addition, it can be concluded that the proposed system is significantly improved the predicting solar activity performance at acceptable assessment indices.