Identifying anomalies from data has attracted increasing attention in recent years due to its broad range of potential applications. Although many efforts have been made for anomaly detection, how to effectively handle high-dimensional data and how to exactly explore neighborhood information, a fundamental issue in anomaly detection, have not yet received sufficient concerns. To circumvent these challenges, in this article, we propose an effective anomaly detection method with representative neighbors for high-dimensional data. Specifically, it projects the high-dimensional data into a low-dimensional space via a sparse operation and explores representative neighbors with a self-representation learning technique. The neighborhood information is then transformed into similarity relations, making the data converge or disperse. Eventually, anomalies are discriminated by a tailored graph clustering technique, which can effectively reveal structural information of the data. Extensive experiments were conducted on ten public real-world datasets with 11 popular anomaly detection algorithms. The results show that the proposed method has encouraging and promising performance compared to the state-of-the-art anomaly detection algorithms.