To solve the problem that energy integration cannot be realized effectively due to the range migration and Doppler migration of the echo of high-speed maneuvering targets, this paper proposes an algorithm of coherent integration via the Second-order Keystone-Biorthogonal Fourier Transform (SKT-BFT) based on velocity compensation.Firstly, a phase compensation function of velocity is constructed to correct the linear range migration caused by velocity by searching the velocity.Secondly, the second-order Keystone transform is used to correct the range bending caused by acceleration, which can also be called second-order range migration.Finally, the slow temporal-dimension signal is regarded as a Linear Frequency Modulation (LFM) signal, and the energy integration is realized by using the biorthogonal Fourier transform to estimate the chirp slope.It can be proved by simulation that this method can effectively realize the integration under the condition of low Signal-to-Noise Ratio (SNR) and the detection of a single target and multiple targets, which has better performance than other algorithms.