Radon-Fourier transform (RFT) is an optimal method for rectilinearly moving targets to overcome range migration with good coherent integration performance in radars. However, it is computationally burdensome because it jointly searches over the range and velocity domains. In this letter, a novel efficient range migration compensation method is proposed. In this algorithm, residual velocity is searched instead of whole velocity range and then a novel low-complexity Doppler ambiguity compensation procedure is executed to search for Doppler ambiguity factor. Compared to the RFT method, the proposed method can achieve a similar detection performance with lower computational cost. Simulation results are provided to verify the effectiveness of the proposed algorithm.