Automatic target detection is an important application in the hyperspectral image processing field. Most statistics-based detection algorithms use second-order statistics to construct detectors. However, for target detection in a real hyperspectral image, targets of interest usually occupy a few pixels with small population. In this case, high-order statistics could characterize targets more effectively than second-order statistics. Also, the inherent variation of spectra of targets is an obstacle to successful target detection. In this paper, we propose a regularized high-order matched filter (RHF) which uses high-order statistics to build an objective function and uses a regularized term to make the algorithm robust to target spectral variation. A gradient descent method is used to solve this optimization problem, and we obtain the convergence properties of the RHF. According to the experimental hyperspectral data, the results have shown that the proposed algorithm performed better than those classical second-order statistics-based algorithms and some kernel-based methods.