Range Cell Migration Correction (RCMC) represents an important advance in moving target imaging in the airborne single antenna high-resolution SAR system. In this paper, we propose a new four-step RCMC approach combined with parameter estimation that overcomes the drawbacks of high computation and low accuracy in high-resolution. First, we use the Hough transform and the energy balancing method to estimate the range velocity and correct the range walk. Next, we perform a range curvature correction in the range-Doppler domain by using the initial Doppler rate. Thirdly, we accurately estimate the Doppler rate using Mapdrift technology. Finally, we correct the residual range curvature by the accurate Doppler rate. Compared with traditional algorithms, the proposed method requires less computation and is robust in the high-resolution SAR system. In this paper, we present a mathematical model and validate its effectiveness using both simulation and real data.