Disturbance storm time index (Dst) is nonlinearly related to solar wind data. In this paper, Dst past values, Dst derivative, past values of southward interplanetary magnetic field, and the square root of dynamic pressure are used as inputs for modeling and prediction of the Dst index, especially during extreme events. The geoeffective solar wind parameters are selected depending on the physical background of the geomagnetic storm procedure and physical models. A locally linear neurofuzzy model with a progressive tree construction learning algorithm is applied as a powerful tool for nonlinear modeling of Dst index on the basis of its past values and solar wind parameters. The result for modeling and prediction of several intense storms shows that the geomagnetic disturbance Dst index based on geoeffective parameters is a nonlinear model that could be considered as the nonlinear extension of empirical linear physical models. The method is applied for prediction of some geomagnetic storms. Obtained results show that using the proposed method, the predicted values of several extreme storms are highly correlated with observed values. In addition, prediction of the main phase of many storms shows a good match with observed data, which constitutes an appropriate approach for solar storm alerting to vulnerable industries.