Compressed Sensing (CS) has been proved to be effective in Synthetic Aperture Radar (SAR) imaging. Previous CS-SAR imaging algorithms are very time consuming, especially for producing high-resolution images. In this study, we propose a new CS-SAR imaging method based on the well-known omega-K algorithm, which is precise and convenient to use in SAR imaging. First, we derive an inverse omega-K algorithm to directly obtain echoes without any convolution between the transmitted signal and scene. Then, we formulate the SAR imaging problem into a sparse regularization problem and solve it using an iterative thresholding algorithm. With our derived inverse omega-K algorithm, we can save significant amounts of computation time and computer memory usage. Simulation results show that the proposed method can effectively recover SAR images with much less data than that required by the Nyquist rate.