Abstract: By applying the monthly Nino 3 index and the NCEP/NCAR re-analysis data covering 60 years from 1950 to 2009, with focusing on the coupling relationship between the 3-5 year timescale stronger ENSO events and the inter-annual variability of the stratospheric circulation, the diagnosis on the 11 ENSO events belonged to 3 stronger ENSO periods are made and the results show that, the winter polar jet tends to anomalously weaken/strengthen after warm/cold ENSO events, and the maximum anomalies appear in the next winter after the ENSO peak; this delayed coupling relationship in the timescale of 3-5 year is particularly consistent during the 3 stronger ENSO periods, and the stronger the ENSO peak, the stronger the stratospheric polar jet anomalies that appear about 1/4 period later. On average, this inter annual timescale response of the stratospheric circulation to ENSO has significant effect on the intensity or polarity of the seasonal timescale Polar Vortex Oscillation. Further diagnosis on the anomalous planetary wave activity in the inter-annual timescale shows that, in the concurrent winter of ENSO peak, an inter-annual timescale PNA (Pacific North America) pattern is excited, while the anomalous PNA excited by cold ENSO is with opposite polarity to that by warm ENSO. The PNA pattern is related to the increasing in the planetary wave-number one in the extra-tropical stratosphere in the concurrent winter. In the next winter, the PNA decays and stronger anomalies exist largely in the mid-high latituds in the upper troposphere. Meanwhile, the planetary wave-number two in the stratosphere is significantly intensified, corresponding to the strongest anomalies of the polar vortex then. However, the contribution of the anomalous convergence of the meridional eddy heat flux and the momentum-flux exhibits quite distinct difference among the different periods. The two factors may contribute either jointly in some periods or separately in other periods.