Unmanned aerial vehicles (UAVs) are increasingly adopted to perform various military, civilian, and commercial tasks in recent years. To assure the reliability of UAVs during these tasks, anomaly detection plays an important role in today s UAV system. With the rapid development of AI hardware and algorithms, leveraging AI techniques has become a prevalent trend for UAV anomaly detection. While existing AI-enabled UAV anomaly detection schemes have been demonstrated to be promising, they also raise additional security concerns about the schemes themselves. In this paper, we perform a study to explore and analyze the potential vulnerabilities in state-of-the-art AI-enabled UAV anomaly detection designs. We first validate the existence of security vulnerability and then propose an iterative attack that can effectively exploit the vulnerability and bypass the anomaly detection. We demonstrate the effectiveness of our attack by evaluating it on a state-of-the-art UAV anomaly detection scheme, in which our attack is successfully launched without being detected. Based on the understanding obtained from our study, this paper also discusses potential defense directions to enhance the security of AI-enabled UAV anomaly detection.