Speeding is one of the most prevalent contributing factors in traffic crashes. The prediction of speeding is important to reduce excessive speeds and prevent speeding-related traffic accidents and injuries. Speeding (either intentional or unintentional) is a consequence of inappropriate speed control. This paper extends a previous mathematical model of driver speed control to provide quantitative predictions of intentional and unintentional speeding. These predictions consist of the time at which the driver exceeds the speed limit and the magnitude of speeding. Based on these modeling predictions, this paper develops an intelligent speeding prediction system (ISPS) to prevent the occurrence of speeding. An experimental study using a driving simulator is conducted to evaluate the ISPS. We find no significant difference between modeled predictions and experimental results in terms of the time and magnitude of intentional speeding. In addition, the ISPS can successfully predict the majority of unintentional speeding instances, with only a small portion of unnecessary speeding warnings. Applications of the ISPS to reduce driving speed and prevent the real-time occurrence of speeding and speeding-related traffic accidents are discussed.