Stock index time series may allow investors to become aware of the change of stock market. In the paper, we aim at forecasting S&P 500 Index, one of the most representative stock indices in United States. A self-organizing fuzzy-based approach for intelligent predictor is used. The design for the predictor is divided into the structure and parameter learning stages. The FCM-Based Splitting Algorithm is used to determine the optimal number of fuzzy rules for the predictor. Two hybrid learning algorithms, the PSO-RLSE and PSO-RLSE-PSO methods, are used for the parameter learning of the predictor, respectively. To test the proposed approach, we devise experiments to compare the performances by the intelligent predictor trained with the two learning algorithms, respectively. Moreover, an additional experiment for different input orders is conducted to see the influence on the performance. The excellent performances in accuracy by the proposed intelligent approach are exposed.