This paper proposes a fast inverse synthetic aperture radar (ISAR) motion compensation (MOCOM) method. The various motion compensation methods using minimum entropy algorithm such as stage-by-stage approaching (SSA) algorithm were reported recently. However, the computational efficiency and the clearance of the ISAR image were hard to achieve simultaneously. In particular, as the number of the local minima in the entropy curve increases, the processing time takes longer to find the global minimum. In this paper, we propose a new MOCOM algorithm based on an improved SSA algorithm to reduce the processing time. The proposed algorithm uses the envelope value as the fitness function instead of the entropy value, so the number of the local minima in the entropy curve is reduced. Therefore, the entropy curve becomes simple and the required number of the phase error samples is reduced. In the simulation, the processing time is improved by 88.8% than the conventional SSA algorithm. Also, in the experiment, the processing time is improved by 87.9% similar to 89.2%.