Equipped with a monopulse antenna, airborne synthetic aperture radar (SAR) gains the ability to detect the ground slowly moving targets. This paper focuses on the constant false alarm rate (CFAR) detection of moving targets for monopulse-SAR. The statistics of complex monopulse ratio (CMR), under complex Gaussian clutter-plus-noise background, is examined in detail when target present or absent. Based on that, a two-step CFAR detector with the probability of false alarm (PFA) given in a closed-form expression for moving target detection is presented and extended to a so called multi-complex monopulse diagram (CMD) form to further improve the final detection performance. Experimental results obtained from two groups of measured dataset are presented to examine the detection performance and validate the theoretical analysis.