Using the NCEP/NCAR monthly mean reanalysis data from 1980 to 2009,this paper investigates the weakening trends of enstrophy in troposphere of Northern Hemisphere under background of global warming.Results show that the enstrophy has a weakening trend in the Northern Hemisphere from 1980 to 2009,especially in the North Pacific and polar regions.The zone of 12.5-50°N is the key area of enstrophy change in the Northen Hemiphere.Changes of the subtropical westerly jet in association with the meridional gradient of air temperature show that the jet intensity has a weakening trend,which is in accordance with the enstrophy change.A vector E is employed to diagnose the Rossby wave propagations in the atmosphere,showing that the disturbances in the atmosphere elongate more meridional in the Northern Hemisphere except western Europe.The meridional eddy heat fluxes in the Northen Hemiphere have also been weakening in the past 30 years.These results are helpful for our better understanding the circulation changes and the influences of global warning.