Due to the large aperture imaging of the Frequency Modulation Continuous Wave Circular Synthetic Aperture Radar (FMCW CSAR) wavenumber domain imaging algorithm, the target scattering coefficient changes, so that the imaging cannot be focused. To solve this problem, a sub-aperture FMCW CSAR fast circular convolution imaging algorithm is proposed, and non-uniform Fourier transform is used instead of interpolation to improve imaging efficiency.At the same time, the FMCW CSAR Doppler process is analyzed, and the principle of subaperture division is deduced theoretically. The expression of subaperture selection is given. The simulation analysis shows that the algorithm can effectively avoid the difficulty of combining the wavenumber domain algorithm with the subaperture. The results show that better imaging is possible within the aperture, and it is difficult to achieve good focus imaging beyond the sub-aperture range.