Clutter suppression plays an important role in a synthetic aperture radar (SAR) system. The conventional SAR imaging methods are useful for distinguishing the echo signal and noise, but cannot separate the target signal from background clutter. Inspired by the signal separation ability of morphological component analysis (MCA), a novel SAR imaging method based on MCA is proposed to suppress the strong background clutter. In the new model, the SAR echo is considered as a linear superposition of target signal, clutter signal, and noise. According to different characteristics of morphological components, clutter dictionary and target dictionary are constructed to sparsely represent the clutter component and target component, respectively. Then, the MCA method based on the sparse representation and morphological diversity of signals is employed to decompose the SAR echo into the target signal, clutter signal, and noise. Finally, the separated target signal is processed to obtain the ultimate SAR image. Experimental results from simulated and real SAR data are provided to demonstrate the effectiveness of the proposed method.