This paper considers the coherent integration detection problem for high speed maneuvering target with a constant jerk, and proposes a new coherent integration detection method involves Keystone transform (KT) and cubic phase function (CPF). Specifically, it employs KT to correct the effect of the range migration. Then, the estimates of the acceleration and jerk with CPF are obtained to compensate Doppler frequency migration. Finally, Fourier Transform (FT) is conducted to integrate coherently the target returns. Compared with the third-order RFT algorithm [8, 10], the proposed method can avoid the problem of blind speed lobe (BSSL) and has a much lower computational complexity under the premise that the two methods have similar coherent integration performance. We evaluate the performance via several numerical experiments.