We consider the coherent detection problem for maneuvering targets with jerk motion. The range migration and Doppler frequency migration are addressed within the coherent interval. An efficient coherent integration method based on time reversal transform (TRT) and scaled nonuniform fast Fourier transform (SNuFFT) is proposed. First, the effects of velocity and jerk are eliminated by multiplying the signals before and after TRT operation. Then, the SNuFFT is newly defined to achieve coherent integration. In comparison with several existing methods, the proposed method has much lower computational complexity by employing fast Fourier transform and nonuniform fast Fourier transform, which guarantees the real-time processing. Simulations and real data processing results validate the effectiveness of the proposed method.