To reduce the storage and transmission burden of massive hyperspectral data as well as keep detecting the anomaly targets accurately and rapidly, a novel non-causal real-time anomaly detection algorithm based on sliding array window is proposed. During receiving the data pixel-by-pixel, the array window slides and determines the local background pixels; and according to the Woodbury lemma, the computation of the matrix inverse of local background can be replaced by the vector multiplication and matrix additions equivalently, then the anomaly pixel in the center of the sliding array window would be detected when receiving the data pixel-by-pixel. The experiments on synthetic and real-world hyperspectral images demonstrate that, compared with several existing real-time detection methods, the proposed method can improve the performance of detection accuracy or computational efficiency. Compared with the non-real-time sliding array RXD anomaly detector, the proposed algorithm has a lower time complexity, and the speedup ratio is nearly 26 times when processing an image with 200×200 pixels and 189 bands. Experimental results verified that the proposed algorithm could maintain the detection accuracy as well as meet the real-time requirements of low computational complexity and low storage space.