Long-time coherent integration (LTCI) is an effective way for radar maneuvering target detection, but it faces the problem of many search parameters and large amount of calculation. Realizing the simultaneous compensation of the range and Doppler migrations in complex clutter background, and at the same time improving the calculation efficiency have become an urgent problem to be solved. The sparse transformation theory is introduced to LTCI in this paper, and a non-parametric searching sparse LTCI (SLTCI) based maneuvering target detection method is proposed. This method performs time reversal (TR) and second-order Keystone transform (SKT) in the range frequency & slow-time data to complete high-order range walk compensation, and completes the coherent integration of maneuvering target across range and Doppler units based on the robust sparse fractional Fourier transform (RSFRFT). Theoretical analysis shows that the proposed method does not require multi-dimensional motion parameters search and matching calculation, which greatly reduces the computational burden, and can compensate for the nonlinear range migration caused by high-order motion. The results using S-band radar data measured in sea clutter background shows that the detection performance of the proposed method is better than MTD, FRFT, Radon Fourier transform, and Radon-FRFT, and thus realizing the rapid integration and detection of maneuvering targets.