The detection of maneuvering targets is a challenging work for radar system. During a long integration time, the target's complex motion will cause severe range migration and Doppler frequency migration, which greatly degrade the energy integration performance. In order to obtain a well-focused result of the maneuvering target, this paper proposes a novel and fast algorithm without any parameter searching process. In our algorithm, a parameter separation (PS) operation is conducted to isolate the target's acceleration from other motion parameters. Then, the second-order keystone transform (SOKT) is utilized to correct range curvature and relocate the target's energy into one range cell. Lastly, the target's energy is integrated along the slow time axis via performing the non-uniform sparse Fourier transform (NUSFT), which is a fast implementation of Fourier transform (FT) for the input signal with unequally sampled points and frequency domain sparse representation. According to the simulation results, the proposed PS-SOKT-NUSFT method can realize multiple targets detection due to its good ability to suppress cross terms. In addition, the runtime of PS-SOKT-NUSFT (106.23 s) is much shorter than the PS-acceleration search (AS) method (2168.67 s).