Long-term coherent integration is an effective method for target detection. However, the inevitable motion compensation errors and complex background clutter seriously limit the detection performance of a cell-averaging constant false alarm rate (CFAR) detector. A generalized CFAR detector on the Riemannian manifold of Hermitian positive-definite matrix is proposed. Based on the α log-determinant divergence (α-LDD) and symmetrized α-LDD, the mean matrix of the reference cells is first estimated. Then the dissimilarity between the covariance matrix of the cell under test and the mean matrix is measured to determine the presence of a target. Numerical experiments show that the proposed detectors have better detection performance than other representative methods when detecting a target with motion compensation errors in complex background.