High-resolution inverse synthetic aperture radar (ISAR) imaging of fast rotating targets is a complicated task. Targets’ fast rotational motion always introduces migration through range cells (MTRC) when we use the conventional range Doppler algorithm. We mainly focus on the ISAR imaging of a fast rotating target. In that case, the samples in the cross-range dimension are insufficient, which is the undersampling case. Compressed sensing-based ISAR imaging methods are generally faced with the problem of basis mismatch, which may degrade the ISAR image. A two-dimensional iterative reweighted super-resolution algorithm is proposed by iteratively decreasing a surrogate function. We also compared the performance of the proposed method with other state-of-the-art sparse recovery methods. Simulation results show that the proposed method can achieve the high-resolution ISAR imaging of fast rotating targets. Moreover, the MTRC and the basis mismatch problems can be effectively solved.