Radar target detection is often faced with complex clutter characteristics. Classical detection methods are usually suitable for some specific scenarios. However, if the detection background changes, its detection performance will suffer from a great degradation. In order to effectively improve the detection performance under different clutter backgrounds, this paper proposes a matrix information geometric detector based on manifold ISOmetric MAPping(ISOMAP). This method first reformulates the problem of signal detection into a discriminative problem between two points on the matrix manifold; then, according to the training sample data and local isometric mapping, a projection matrix is adaptively learned, which transforms the matrix manifold into a discriminative low-dimensional manifold to enhance the separability between the target and the clutter; finally, the proposed algorithm is verified by simulated clutter and measured data. Experimental results show that the proposed method can effectively improve the detection performance in comparison with the classical detectors.