Target detection in clutter is a fundamental problem in radar signal processing. When the received radar signal contains only few pulses, it is difficult to achieve a satisfactory performance using the traditional detection algorithm. In recent times, a generalized constant false alarm rate (CFAR) detector on the Riemannian manifold of Hermitian positive-definite (HPD) matrix was proposed. The employment of this detector, which compares the Riemannian distance between the covariance matrix of the cell under test (CUT) and an average matrix of reference cells with a given threshold, has significantly improved the detection performance. However, the application of this detector in real scenarios is still limited by two problems; it is computationally expensive and the detection performance is not very good since the Riemannian distance is utilized. In this paper, the symmetrized KullbackLeibler (sKL) and the total KullbackLeibler (tKL) divergences, instead of the Riemannian distance, are used as dissimilarity measures in the matrix CFAR detector. According to sKL and tKL divergences, three average matrices, the sKL mean, the sKL median, and the tKL t center, are derived. Furthermore, the relationship between the detection performance and the anisotropy of the distance measure used in the matrix CFAR detector is explored. Numerical experiments and real radar sea clutter data are given to confirm the superiority of the proposed algorithms in terms of the computational complexity and the detection performance.