The influences of transverse wind on the light propagation path in the horizontal atmosphere and on the performances of an ideal compensation system and an adaptive optics system with finite time bandwidth are analyzed theoretically. The analytical expression of Strehl ratio of adaptive optics system vs. the transverse wind speed has been obtained. The calculated results show that transverse wind has strong influence on the performance of an adaptive optics system. As the transverse wind speed increases, Strehl ratio of the system decreases quickly. for the adaptive optics system with certain aperture size, the image of the compensated light is worse than that of the uncompensated light while transverse wind speed exceeds a threshold value. Considering the physical structure of the atmospheric turbulence, the phenomenon has been analyzed and explained.