As an all-day and all-weather senor, synthetic aperture radar (SAR) has won widely applications on many fields. Recently, ground moving target indication (GMTI) and moving target imaging have attracted many attentions in SAR, which may dramatically extend the functions and applications of conventional SAR . However, people have also recognized that it is challenging for SAR to determine the moving target from the strong stationary ground clutter. Because of the radar’s down-looking and wide beam to synthesize a large aperture, the target in a certain range bin will compete with the azimuth-distributed ground clutter and the signal-to-clutter ratio (SCR) of raw echoes is normally extremely low in raw signal domain. Furthermore, due to the fast motion of the platform, the distributed clutter will generate a Doppler-distributed spectrum and target will be “submerged” in Doppler domain. Therefore, the conventional moving target indication (MTI) method in a short coherent integration time, widely used by ground-based radar, may be invalidated for SAR. In order to utilize the clutter’s coupling property, between spatial distribution and Doppler information, to better suppress clutter of moving platform, some SAR systems based on multiple channels have been proposed. In a short coherent time, the space-time adaptive processing (STAP)  or displaced phase center antenna (DPCA) has been proposed to dramatically suppress clutter and improve moving target detection performance. In raw signal or image domain of a long coherent time, some effective methods, e.g., space-time-frequency processing , along-track interferometric SAR (ATI-SAR)  and velocity SAR (VSAR) [4,5], have also been proposed. Unfortunately, above these effective methods may be only applicable for the SAR equipped with multiple channels. However, most of existing SAR, e.g., the spaceborne SAR as RadarSAT-I, owns only a single channel for receiving and their output is the complex image product. How to determine whether the targets are existed, as well as how to refocus and relocate them in the complex image, become the interesting and essential problems. It is well known that the unmatched phase errors of the moving targets may bring about a mis-located and unfocused imaging result in cross-range in the final image . Besides, the uncompensated “range migration” will also blur the moving targets in slant-range. Fortunately, even via the imaging processing with respect to the static scene, the amount of clutter competing with target may be relatively reduced because target is partially matched. As a consequence, the SCR will be remarkably increased in a certain pixel compared to that of raw echoes. On the other hand, the appearance of moving target may be different from static scatterer the in the image domain. In this paper, we first propose a novel single-channel SAR moving target signal model in the complex image domain, based on the frequency-domain azimuth focusing and stationary phase principle (SPP). The moving target’s signal model may also be regarded as a LFM but distributed in a two-dimensional (2-D) area, and the unknown LFM parameters, i.e., Doppler center and Doppler rate, may be closely related with the target’s 2D motion . Therefore, based on the accurate estimation the Doppler parameters, the motions of moving target may be also obtained to refocus and relocate them. Furthermore, based on the maximum likelihood (ML) methods, we derive the Cramer-Rao Bounds (CRB) for the unknown parameter. The numerical experiments based on the typical SAR system parameters are also provided to verify the proposed signal model and the ML methods. This paper is organized as follows. In section 2, the static scatter and moving target in complex image domain are analyzed and a novel signal model is proposed. In section 3, the Doppler parameter estimation based on maximum likelihood (ML) methods are discussed and the Cramer-Rao bounds are derived. In section 4, the performance analyzes are provided based on numerical experiments. In section 5, some useful conclusions are drawn.