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Narrow-band interference (NBI) is a common interference source in synthetic aperture radar (SAR) imaging. Its existence will degrade the imaging quality greatly. Based on detailed analysis on the characteristics of NBI, this letter proposes a new NBI suppression algorithm using the complex empirical mode decomposition (CEMD) method. In this algorithm, echoes that include NBI are recognized in the time domain first. Then, these echoes are decomposed into a number of intrinsic mode functions (IMFs) via the CEMD. After that, IMFs that correspond to NBI are subtracted from the echoes by thresholding. Finally, well-focused SAR imagery can be obtained from the separated target echoes using traditional SAR imaging algorithms. The effective data loss in this algorithm is smaller than other NBI suppression approaches. In addition, this algorithm is robust to time-varying NBI. Imaging results of measured data have proved the validity of this algorithm.