In order to further improve the capabilities of clutter suppression and target detection in airborne multiple-input multiple-output (MIMO) radar space-time adaptive processing (STAP), the polarization-space-time adaptive processing (PSTAP) method based on polarization array MIMO radar is proposed. Firstly, by applying the novel polarization array to airborne MMO radar, the signal model of airborne polarization array MIMO radar PSTAP is established. Then based on the idea of resolution grid, the influence of clutter can be equivalent to the formation of independent point sources of clutter related to the clutter degree of freedom, and an equivalent expression for the covariance matrix in polarization array MIMO radar PSTAP is obtained. Next, combined with the equivalent covariance matrix, the signal-to-clutter-plus-noise ratio (SCNR) performance of the polarization array MIMO radar PSTAP is derived and analyzed. The effects of the polarization, spatial and temporal matching coefficients are discussed. When the target is located in the side-looking direction of the airborne radar, the normalized spatial frequency of the target is zero. Then the spatial transmit and spatial receive matching coefficients between the target and the clutter point source in the center of the space-time plane both approach to one. Meanwhile, the normalized Doppler frequency of the side-looking target is in direct proportion to the target speed. When the target speed decreases to zero, the temporal Doppler matching coefficient between the target and the central clutter source is near to one. Thus taking the spatial and temporal matching coefficients into consideration, the SCNR loss of the traditional MIMO-STAP is approximate to zero. It indicates that for traditional MIMO-STAP, its performance of detecting low-speed target is severely degraded by the clutter source, and target detection can hardly be realized just in space-time domains. However, through utilizing the additional polarization information to take advantage of the polarization matching coefficient, the polarization array MIMO radar PSTAP increases the SCNR loss and remarkably lessens the influence of the central clutter source. According to the above theoretical analysis, we can come to the conclusion that the polarization array MIMO radar PSTAP can effectively promote the capability of clutter suppression compared with the traditional MIMO-STAP, which is beneficial to the detection of the moving target with low-speed. Moreover, the improvement of output SCNR performance becomes more significant with increasing the differences between the polarization parameters of target and those of clutter. Therefore, the polarization array MIMO radar PSTAP has great application value for practical engineering. The simulation results verify the validity and superiority of the proposed polarization array MIMO radar PSTAP method.