Abstract: According to the problem of the ‘three crossing’ motions and compensations for the ground moving target of high speed moving multi-input and multi-output (MIMO) radar, a space model is established and the equations of delay and transmit pattern which is changing with time and period are educed. The echo characteristics are analyzed and the formulas of ‘three crossing’ are derived. A compensation method is proposed by using pre-process to compensate crossing range-cell and crossing-beam and by applying FrFT to compensate crossing Doppler-cell. The method could compensate ‘three crossing’ simultaneously with much less calculating quantities than methods presented before as pre-process of the transmit signals. At last, the phantom antenna array is used in the simulations, and the ‘sparse transmit dense receive’ is applied to the simulation of crossing-beam and its compensation. The results of simulations demonstrate the validity of the method combining pre-process and FrFT to compensate ‘three crossing’.