As a new kind of intelligent vehicle, Connected and Automated vehicles (CAVs) can provide more convenient service by exchanging data with other vehicles and roadside units. However, CAVs rely heavily on the sensor data and communicated information. Negative factors such as faults, e1rrors, or network attacks may lead to serious consequences. To avoid the aforementioned situation, this paper proposes a method for time-series anomaly detection in CAVs. Firstly, we process the data by performing a moving standard deviation and maximum minimum normalization transformation. Then, a WGAN network with gradient constraints is constructed to perform real-time anomaly detection. We conducted experiments on the Safety Pilot Model Deployment (SPMN) dataset. Results have shown that this method can effectively improve the accuracy and sensitivity of detecting different types of abnormal situations. It also works well in detecting less obvious abnormal data.