Abstract: The Compressive Sensing (CS) based SAR imaging method can reduce the sampling time, the data volume and save signal band width. However, the CS based methods are sensitive to noise and clutter. In this paper, a new imaging modality based on Bayesian Compressive Sensing (BCS) is proposed along with a novel compressed sampling scheme. This new imaging scheme requires minor change to traditional used system and allows both range and azimuth compressed sampling. Also, the Bayesian formalism accounts for additive noise encountered in the compressed measurement process. Experiments are carried out with noisy and cluttered imaging scenes to verify the new imaging scheme. The results indicate that the Bayesian formalism can provide a sharp and sparse image absence of side-lobes which is the common problem in conventional imaging methods and have fewer artifacts compared to the previous version of CS based methods.