The Kp geomagnetic activity index is an important indicator of geomagnetic disturbances, which mark adverse space weather conditions affecting space missions and causing satellite anomalies. Therefore accurate Kp prediction is essential for warning and alert systems. A black box model, based on a recently developed locally linear neurofuzzy model, is proposed to reconstruct the highly nonlinear and complex dynamics of the magnetosphere. While most of the previous studies have investigated input-output models of the solar wind--driven magnetosphere, this network is trained to use only nine previous observations of Kp time series to reconstruct the internal dynamics and to predict the forthcoming Kp values of the test years (from 1991 to 2000). The incremental learning algorithm initializes the model with an optimal linear least squares estimation and automatically increases the number of neurons in each epoch. The model is optimized for the number of neurons to avoid overfitting and to provide maximum generalization by considering the error index of validation sets during training. The obtained results, for example, RMS error of 0.84 and correlation factor of 0.807 between the predicted and observed values, are superior in comparison with previous studies. The rate of correct, missed, and false detections for related warning messages are also calculated and reported.