Airborne Ultra-Wide Band Synthetic Aperture Radar (UWB SAR) has larger integrated angle and longer synthetic aperture, which gives rise to more complexity in motion errors. In light of this, first the motion model of airborne UWB SAR was derived. Then, the expression of echo spectrum in presence of motion error was deducted. Theoretic analysis on the reason of the motion error impacts on SAR imaging and the influences on SAR images induced by the different motion errors were carried out. Experiment results on simulated data proved the validity of the theory analysis presented in this paper.