Anomaly detection is an important application of hyperspectral images. Aiming at the problems in current researches, a new anomaly detection algorithm based on spectral analyses was proposed for hyperspectral images. The algorithm used spectral analyses technique to effectively separate target information from complicate backgrounds and greatly suppressed background interferences for detection. And those error data obtained after spectral unmixing with background endmembers only include abundant target information and better follow Gaussian distribution. Principal component analysis was used to transform the error data, and local average singularity was defined to select the most effective principal component for anomaly detection according to high-order statistics. Final detection was realized with conventional RX detector. To validate the effectiveness of the proposed algorithm, numerical experiments were conducted on real AVIRIS data. Experimental results show that the proposed algorithm greatly outperforms the conventional RX algorithm.