Hyperspectral anomaly detection is a research hot spot in the field of remote sensing. It can distinguish abnormal targets from the scene just by utilizing the spectral differences and requiring no prior information. A series of anomaly detectors based on Reed-Xiaoli methods are very important and typical algorithms in this research area, which generally have the hypothesis about background subject to the Gaussian distribution. However, this assumption is inaccurate to describe a hyperspectral image with a complex scene in practice. Besides, due to the unavoidable existence of abnormal targets, background statistics will be affected which will reduce the detection performance. To address these problems, we propose a sparse dictionary learning method by using a capped norm to realize hyperspectral anomaly detection. Moreover, a new training data selection strategy based on clustering technique is also proposed to learn a more representative background dictionary. The main contributions are concluded in threefold: 1) neither making any assumptions on the background distribution nor computing the covariance matrix, the proposed method is more adaptive to all kinds of complex hyperspectral images in practice; 2) owing to the good qualities of the capped norm, the learned sparse background dictionary is resistant to the effect of anomalies and has stronger distinctiveness to anomalies from background; 3) without using the traditional sliding hollow window technique, the proposed method is more effective to detect different sizes of abnormal targets. The extensive experiments on four commonly used real-world hyperspectral images demonstrate the effectiveness of the proposed method and show its superiority over the benchmark methods.