Recently, vehicle classification is becoming increasingly important with the development of automated driving technology. In particular, it can provide the basis and prerequisites for autonomous vehicles to make decisions in terms of improving driving safety. However, the current mainstream vehicle classification methods are deep learning algorithms based on Convolutional Neural Networks (CNN), which are mainly focused on the cloud, and these algorithms have complex models and large training parameters. In addition, for computationally intensive and urgent tasks, the poor computational power and low storage capabilities of edge nodes cannot support CNN-based vehicle classification algorithms for model updating. In this paper, we propose a lightweight vehicle classification method with mobile edge computing based on Broad Learning System (BLS). On the one hand, the vehicle can serve as a mobile edge computing node to provide computing and storage resources to ensure that classification tasks are performed locally and quickly, avoiding the bandwidth congestion caused by uploading to the cloud. On the other hand, we use broad learning method to perform incremental training on the data, which is more suitable for computing at the edge, because it can support incremental updates to the model on the vehicular edge nodes without retraining the whole model. Experiments are conducted on a Raspberry Pi system to simulate edge nodes, the results show with a similar performance, the training speed of our vehicle classification system can be increased by 10 times compared with the other CNN-based algorithms.