Abstract: The spiral rain bands of tropical cyclone and the vortex Rossby waves are reviewed.It is pointed specially that the axisymmetrizing disturbances on a vort exare accompanied by out ward-propagating vortex Rossby waves whose restoring mechanism is associated with the gradient of storm vorticity,for the goal of elucidating the dynamics of outward-propagating spiral bands in tropical cyclone.The theoritical value of its outward-propagating speed is about O(10 m/s),almost to be consistent with observational one of spiral rain bands.Based on the principle of conservation of vorticity(or PV),the restoring mechanism of vortex Rossby wave is equivalent dynamically to the planetary Rossby wave.