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When multiple radar targets are close to each other, the returned signals from these targets are overlapped in time. The translational motion can be viewed as a uniformly accelerated motion, therefore, the Doppler variation of echoes in the cross-range direction can be approximated by the first-order polynomial which is called linear frequency modulation signal. For different targets, the chirp rates are different from each other. In this paper, a new algorithm based on fractional Fourier technique is proposed to separate the signals from different targets in each cross-range cell. By the CLEAN technique, the number of targets need not be specified. We derive original algorithms to compensate the motion of each target signal, so the image of each target can be obtained. The simulation results are given to demonstrate the efficiency of the proposed algorithm for multiple moving targets imaging.