Radar has been regarded as the enabling sensor technology to realize the intelligent transportation system. The current works in traffic radar mainly focus on detecting the target with fixed size. However, traffic scenarios consist of various targets with different sizes. Therefore, in this paper, we propose a CenterNet-based radar signal processing framework for detecting and classifying four types of traffic targets on the Range-Doppler map, and illustrate CenterNet can achieve higher detection rate, lower false alarm rate, and better classification performance with the help of the Anchor-free structure, shows the usability of CenterNet for radar detection and classification in traffic scenarios.