To obtain sufficient resolution, the operating band of synthetic aperture radar (SAR) must extend over several tens of megahertz. Consequently, SAR reception occurs across frequency bands allocated for other broadcasting stations and SAR often suffers radio frequency interference (RFI). This study proposes a novel approach to suppress RFI in SAR. The authors combine the classical spectral analysis method singular spectrum analysis, with an efficient subspace tracking method fast approximated power iteration (FAPI) which has the most economical computational cost among state-of-the-art algorithms. Furthermore, they supply a gap of FAPI so that it can achieve rank tracking based on eigenvalues distribution of the covariance matrix of the observed SAR record and in that way can detect the number of RFIs along the SAR azimuth time. The proposed algorithm is a time domain processing method and performs on SAR range records one-by-one. Finally, well-focused SAR imagery is obtained from the 'decontaminated' SAR data using classical SAR imaging algorithms. The proposed algorithm could be applied in complicated interference circumstances no matter the styles of RFI. Imaging results of artificial and real data have proved the validity and robustness of this algorithm.