Synthetic aperture radar(SAR) imaging which use compressed sensing(CS) technology able to restore thetarget image clearly by using less observations date, but the presence of broadband suppress jamming in the echoeswould seriously undermine the sparsity of the scene, resulting in deterioration of image quality. Study an suppression method of broadband suppress jamming by using adaptive compressed sensing which based on selective measurement, the method by constructing a compressed domain projection filter and combined with noise joint detection algorithm to perceived the positional information of interference adaptively, then to selection measurement of the SAR echo signal, and to avoid the influence of interference on the sparsity of SAR echo signal from the "source". The simulation results show that this approach not only reduces the amount of data processing of SAR system, at the same time, making the quality has improved significantly of SAR image, proved the effectiveness of this method.