Compressed sensing (CS)-based inverse synthetic aperture radar (ISAR) imaging with limited pulses performs well in the case of high signal-to-noise ratios. However, strong noise are usually inevitable in radar imaging, which challenges the CS-based approach. In this paper, we present an adaptive noise depression CS-ISAR imaging algorithm, which is based on constant false alarm rate (CFAR). Firstly, the noise level is estimated from the noise range cells which are discriminated by energy thresholding. Then the ISAR images are reconstructed via orthogonal matched pursuit (OMP), in which the iteration is terminated by a preseted residual thresholding (RT). The RT is set according to the estimated noise level for a certain CFAR. Experiments verify the efficiency of the proposed method.