Narrow-band interference (NBI) and Wide-band interference (WBI) are common jamming signals against synthetic aperture radar (SAR), in which the imaging quality can be degraded severely. To effectively suppress NBI and WBI, a novel time-frequency iteration decomposition method is proposed based on ambiguity function iteration decomposition. In this algorithm, echoes contaminated by interferences are identified in the radon ambiguity function (RAF) domain. After that, the masked method and signal synthesis method are utilized to extract and recovery interferences from the ambiguity function. Finally, the reconstructed interferences are subtracted from the echoes, and the well-focused SAR imagery is obtained by conventional imaging methods. The simulation and measured data results demonstrates that the proposed algorithm not only suppresses interference efficiently but also preserves the useful information as much as possible.