Abstract: Radar target detection problem can be processed by a new thinking and method called matrix CFAR detection based on geometry manifold. An enhanced matrix CFAR detection method based on supervised dimensionality reduction of Riemannian manifold is proposed to further improve its performance in complex clutter background in this paper. Firstly, the detection problem is regarded as a classification problem of the target and clutter, and within-class weight matrix and between-class weight matrix of the target and clutter on the Riemannian manifold are constructed, respectively. Then, in order to enhance the discriminability between the clutter and target, an optimal objective function for dimensionality reduction is obtained by maintaining the minimum within-class geometry distance and the maximum between-class geometry distance, and an explicit mapping matrix can be obtained by solving the optimization problem on Grassmann manifold. Finally, an enhanced matrix CFAR detection method is proposed for the enhancement detection of the target. By Monte Carlo technique, the experimental results of simulated data and real sea clutter data demonstrate that the proposed method can achieve a better detection performance.