Ice covers in high latitudes play important role in the global atmospheric circulation and abnormal temperature distribution. The observations have revealed the differences in the interannual variability of the Arctic and Antarctic ice covers, but their respective climate effect is not clear. The Liang-Kleeman information flow method is used to reveal the causal relationships from the sea ices of the Arctic and Antarctic to the global air temperature. The results point out that changes of the Arctic or Antarctic sea ices both have significant impacts on the global air temperature. Especially for the air temperature in East Asia and North America, the interannual variation of the Antarctic sea ice has an even stronger impact than the Arctic ice covers. This causality is further proved by the General Atmospheric Circulation Model (CAM4.0). In the numerical experiments, the ice covers in Arctic and Antarctic are changed individually or simultaneously as the forcing fields, and then the respective climate effects are analyzed. The results show that both the Arctic and Antarctic ice cover variations can change the intensity of atmospheric baroclinic disturbance in mid-high latitudes of individual hemisphere, generating wave energy transmission across the equator in the meridional direction, and eventually causing air temperature anomalies in both hemispheres. Furthermore, the Antarctic ice covers are closer to the mid-high latitude atmospheric jets in the southern hemisphere. Therefore, the changes of Antarctic ice covers lead to a larger atmospheric wave-activity flux response, and quickly spread to the northern hemisphere, causing more significant temperature anomalies over the East Asia and North America.