Hyperspectral Remote Sensing technology records radiation signals with spectral information of objects through imaging spectrometers to obtain three-dimensional hyperspectral images containing spectral information and spatial information. It has been widely used in spectral unmixing, image classification, and target detection. In recent years, with the development of remote sensing technology and the increasing demand for accurate location of targets, target detection has achieved rapid development. According to whether the target spectrum is grasped in advance as a priori information, target detection is divided into spectrum matching detection and anomaly detection. Spectrum matching detection requires the target spectrum as a priori information, and usually has higher detection accuracy and better results. The anomaly detection does not require prior information and has a wider application range, but the detection accuracy is usually lower than that of spectral matching detection. Due to the lack of a complete and practical spectral library in practical applications, it is difficult to obtain prior information, and anomaly detection that does not require prior information has become a research hotspot. This paper proposes an Approximate Posterior Information-based Hyperspectral Anomaly Detection Algorithm. First, the matrix decomposition algorithm is used to decompose the original hyperspectral image data to obtain a pure background matrix and an anomaly matrix containing noise. The anomaly matrix is discarded, and the obtained background matrix is used as approximate background information. Then calculate the Mahalanobis distance between the spectral vector of all the pixels in the image and the mean vector in the background matrix to perform initial anomaly detection on the image to obtain the initial anomaly. Finally, the approximate background information and approximate target information are used as prior information, and orthogonal subspace projection is performed to obtain the final anomaly detection algorithm. Applying this algorithm to all the pixels in the image, we get the anomaly detection result for the whole image. In order to prove the excellent effect of this algorithm, a group of simulation data and a group of AVIRIS real hyperspectral data were used for experiments, and compared with RX, LRX, LSMAD algorithms. Experiments show that the algorithm can effectively suppress noise, both from a qualitative perspective and a quantitative perspective, and can still effectively detect anomalous targets in the image when the signal-to-noise ratio is relatively low. The effect of detection efficiency is small, and good detection results have been achieved.