A novel detection method for the high-speed maneuvering multi-target with a constant acceleration is proposed. Firstly, velocity searching and Second-order Keystone Transform (SKT) are jointly applied to correct the range migration (RM). After the RM correction, the azimuth echoes can be considered as a Linear Frequency Modulation (LFM) signal. Secondly, Lv's Transform (LVT) is performed on the azimuth echoes, target energy will be accumulated into a sole peak in the Centroid Frequency (CF)-Chirp Rate (CR) domain, and an estimated acceleration can be obtained in terms of the peak's location in the CR-axis. Finally, according to the estimated acceleration, a compensation function is constructed to compensate the Doppler Frequency Migration (DFM), after that, the FFT is applied to accomplish coherent integration, and then target detection is carried out, meanwhile, the target's radial velocity can be estimated. Compared with the Radon-Fractional Fourier Transform (RFRFT), the proposed algorithm possesses the advantages of lower computational complexity and better anti-noise performance. The results of simulation and real data demonstrate the validity of the proposed algorithm.