With the increasing highlighted security concerns in Intelligent Transportation System (ITS), Vehicle Make and Model Recognition (VMMR) has attracted a lot of attention in recent years. The VMMR method can be widely used in suspicious vehicle recognition, urban traffic monitoring, and the automated driving system. With the development of the Vehicle-to-Everything (V2X) technology, the vehicle information recognized by the AI-based VMMR method can be shared among vehicles and other participants within the transportation system, which helps the police fast locate the suspicious vehicle. VMMR is complicated due to the subtle visual differences among vehicle models. In this paper, we propose a novel Recurrent Attention Unit (RAU) to expand the standard Convolutional Neural Network (CNN) architecture for VMMR. The proposed RAU learns to recognize the discriminative part of a vehicle from multiple scales and builds up a connection with the prominent information in a recurrent way. RAU is a modular unit. It can be easily applied to different layers of the vanilla CNN architectures to boost their performance on VMMR. The efficiency of our models is tested on three challenging VMMR benchmark datasets, i.e., Stanford Cars, CompCars, and CompCars Surveillance. The proposed ResNet101-RAU achieves the best performance 93.81\% on Stanford Cars dataset and 97.84\% on CompCars dataset.