Abstract: The detection performance of the Moving Target Detection　(MTD) method descends badly in a non-Gaussian correlated clutter background. Therefore, a radar target detection method in the non-Gaussian correlated clutter background is proposed, which is obtained based on the alpha-stable distribution clutter model and the eigenfilter. The proposed method suppresses the non-Gaussian clutter by the signed power and whitens the correlated clutter of the fractional lower order correlate matrix, which is based on the alpha-stable distribution clutter model. Finally, the eigenfilter is used to get a higher signal clutter ratio. Simulations and real data results show that, the detection performance of the proposed method obviously outperforms the MTD method in the non-Gaussian correlated clutter background.