Synthetic aperture radar is susceptible to electromagnetic interference by television networks, communication networks and other wireless devices, which seriously damages the image quality. Under the premise of the analysis of the characteristics of interference and signal model, a method of SAR narrowband interference suppression based on compressed sensing was proposed. According to the difference of the FM slope of the SAR echo signal and the narrowband interference signals in the Chirplet dictionary, interference signal was filtrated and suppressed in the reconstruction of the SAR echo signal, and then use the conventional method to achieve the SAR image with the compressed data in which the disturbance is removed away. The simulation results show that the method not only can effectively suppresses narrowband interference, but also greatly reduces the amount of data in SAR imaging processing system, which demonstrate the effectiveness of the proposed method.