The extreme cold and snow weather occurred at the mid-latitudes of Northern Hemisphere in December 2009.Based on the NCEP/NCAR reanalysis data,this paper studies the characteristics of stratospheric AO(Arctic Oscillation) abnormal signal downward propagation and its influence on the extreme weather,and the planetary wave propagation mechanism related to the abnormal signal downward.It shows that:1)The Arctic Oscillation(AO) plays an important role in this cold event,and its anomalous negative signal occurs and maintains in the stratosphere during the preceding November.In the early December,the associated anomalies spread into the troposphere and then propagates fast onto the surface,which leads to remarkably positive(negative) geopotential height and temperature anomalies in the northern polar(mid-latitude) region in the whole troposphere in December.2)Induced by the negative AO signal,the anomalous northerlies dominate the eastern Asia and the west part of the Northern America during the early December,facilitating the extreme cold condition in these areas.The associated northwesterly anomalies in the Europe and the strengthened cold Mongolian high also result in the prevalence of low temperature in the northern Eurasian continent during the mid-to-late December.3)The stationary planetary wave propagation into the stratosphere is extremely strong at the high-mid latitudes of Northern Hemisphere in November,which induces negative AO anomaly in the stratosphere.Accompanied by weakening of the planetary wave upward propagation during the following December,the negative AO anomaly exhibits from the upper troposphere to surface,leading to cold-condition circulation anomalies.