A novel compressed sensing imaging algorithm for high-squint Synthetic Aperture Radar (SAR) based on a Nonlinear Chirp-Scaling (NCS) operator is proposed. First, the echo signal of high-squint SAR is analyzed, and a novel imaging method based on the Nyquist-sampled echo signal is proposed. With the proposed method, the range migration is corrected and the coupling problem in the range and azimuth directions is solved. Then, to solve the problem of high-squint SAR imaging using undersampled echo signals, the NCS operator and compressed sensing algorithm based on this operator are constructed. Imaging results are obtained by solving an optimization problem. The proposed method can recover a sparse scene using undersampled echo data. Furthermore, it can recover a nonsparse scene using fully sampled data. Finally, simulations show the effectiveness of the proposed method.