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The accuracy of background clutter model is a key factor which determines the performance of a constant false alarm rate (CFAR) target detection method. G0 distribution is one of the optimal statistic models in the synthetic aperture radar (SAR) image background clutter modeling and can accurately model various complex background clutters in the SAR images. But the application of the distribution is greatly limited by its disadvantages that the parameter estimation is complex and the local detection threshold is difficult to be obtained. In order to solve the above-mentioned problems, an synthetic aperture radar CFAR target detection method using the logarithmic cumulant (MoLC) + method of moment (MoM)-based G0distribution clutter model is proposed. In the method, G0 distribution is used for modeling the background clutters, a new MoLC+MoM-based parameter estimation method coupled with a fast iterative algorithm is used for estimating the parameters of G0 distribution and an exquisite dichotomy method is used for obtaining the local detection threshold of CFAR detection, which greatly improves the computational efficiency, detection performance and environmental adaptability of CFAR detection. Experimental results show that the proposed SAR CFAR target detection method has good target detection performance in various complex background clutter environments.