Ultra-wideband frequency modulated continuous wave (FMCW) radar has the ability to achieve high-range resolution. Combined with the inverse synthetic aperture technique, high azimuth resolution can be realized under a large rotation angle. However, the range-azimuth coupling problem seriously restricts the inverse synthetic aperture radar (ISAR) imaging performance. Based on the tutable model, traditional match-filter-based, range Doppler algorithms (RDAs) and the back projection algorithm (BPA) are investigated. To eliminate the sidelobe effects of traditional algorithms, compressed sensing (CS) is preferred. Considering the block structure of a signal at high resolution, a block-sparsity adaptive matching pursuit algorithm (BSAMP) is proposed. By matching pursuit and backtracking, a signal with unknown sparsity can be recovered accurately by updating the support set iteratively. Finally, several experiments are conducted. In comparison with other algorithms, the results from processing the simulation data, some simple targets, and a complex target indicate the effectiveness and superiority of the proposed algorithm.