Abstract-Based on the observation that sparsity assumption is well satisfied in the synthetic aperture radar (SAR) imaging applications, there is increasing interest in utilizing compressive sensing (CS) in SAR imaging. However, there are still several problems which should be concerned in CS-based imaging approaches. Firstly, inevitable noise and clutter challenge the performance of CS algorithms. Secondly, the super-resolving ability of CS algorithms is not sufficiently exploited in most cases. Thirdly, nonideal characteristics of mutual coherence affect the performance of CS algorithms in complex scenes. In this paper, a novel CS imaging framework is proposed for the purpose of improving the imaging performance of stepped frequency SAR. Meanwhile, a super-resolving imaging algorithm is proposed based on the nonquadratic optimization technique. Simulated and rail SAR measured data are applied to demonstrate the effectiveness of the novel framework with the proposed super-resolving algorithm. Experimental results validate the superiority of this method over previous approaches in terms of robustness in low SNR, better super-resolving ability and improved imaging performance in complex scenes.