Abstract: The radar target detection performance of the MTD(Moving Target Detection) method descend badly in non-Gaussian correlated clutter backgrounds. Therefore, a radar target detection method in non-Gaussian correlated clutter backgrounds is proposed. The proposed method is obtained by the rule of maximizing the output signal-to-clutter power ratio based on alpha stable clutter distribution model and the fractional lower order statistics. The proposed method obtained the optimum filter coefficient by decomposing the signal fractional lower order covariance matrix and computing the eigenvector of the clutter fractional lower order covariance matrix. Simulations and real data results show that, the detection performance of the proposed method obviously outperforms the traditional MTD method in non-Gaussian correlated clutter environments.