Considering the two issues of range migration and Doppler spectrum extension in the detection of high maneuvering targets in space-air based bistatic radar (SABBR), and on the basis of the establishment of the echo signal model and the analyses of the signal migration feature, a novel target detection algorithm suitable for SABBEWR is proposed. The Keystone transform is used to compensate the range migration in range frequency slow time domain, and the discrete chirp-Fourier transform (DCFT) is modified to estimate the target's acceleration and frequency divisor. A quadratic phase compensation function is constructed to make up for the Doppler migration. The coherent integration is performed for target detection. Simulation results show that the radial acceleration is estimated precisely, the energy of the high maneuvering target is accumulated effectivelly, and the performance detection is improved in low signal to noise ratio background.