Abstract: ‍ ‍A nonlinear frequency offset that increased nonlinearly was added to the radiated signal of each element of a nonlinear frequency diverse array-multiple input multiple output （FDA-MIMO） radar， which changed the “S” shaped range-angle beam pattern of the radar. This focused the transmitted energy into a point beam on the target position and within the effective target range to obtain better target-detection performance. When this type of radar detects a moving target， a Doppler shift occurs in the slow-time dimension because of the frequency-offset coupling between the transmitting array elements and target velocity. A resampling algorithm based on interpolation filtering can compensate for the Doppler shift caused by the frequency offset. However， for the nonlinear FDA-MIMO radar， this will fail because the frequency offset between the elements no longer changes linearly. This study investigated a new algorithm that used keystone transform and Doppler shift compensation methods to detect moving targets with nonlinear FDA-MIMO radar. An echo model of a nonlinear FDA-MIMO radar moving target was established. The cause of distance migration in the moving-target detection was analyzed， and the shortcomings of the resampling algorithm based on interpolation filtering were determined. Then， a velocity search-based algorithm was proposed to compensate for the Doppler shift that occurs when detecting moving targets with nonlinear FDA-MIMO radar. First， the keystone transform was used to eliminate the range migration of the target echo. Then， a Doppler compensation function was constructed based on the frequency offset between the array elements， and a velocity search function was constructed using the Doppler compensation function and echo signals after the pulse compression of each array element. The function was searched after setting an appropriate velocity search range， and when the function reached a peak， the corresponding velocity was the true velocity. Finally， after compensating for the Doppler offset with the searched velocity， coherent accumulation was performed to detect the target. The simulation results showed that the Doppler shift between array elements could be accurately compensated by the proposed algorithm， and its detection performance with the nonlinear FDA-MIMO radar system was better than that of the resampling algorithm based on interpolation filtering.