In this paper, a novel method is proposed to classify drivers in vehicle following behavior. The main contribution of this work is to construct a method to classify drivers as the fundamental model to consider characteristics of each driver under a scene that the target vehicle follows the preceding vehicle. Many methods have been proposed using data-driven approaches, however, each driver has an own driving style and shows different characteristics to be influenced by traffic conditions. As the result, the performance of previous methods to detect common patterns trained by machine learning techniques may realize the limitation. The proposed method extracts a new feature to describe a driving style by using a dynamic potential field method, and it can be a significant feature to classify drivers. It is demonstrated that our new feature dramatically improves the accuracy of driver classification through experimental results.