Abstract: On the basis of the diagnostic analysis of 500hPa height's initial analysis field and forecast field data of T42L9 model of National Meteorological Center(Beijing), forecast skill of cases has been carefully surveyed using statistic method. Two basic results have been obtained a) The forecasting of forecast skill should be done together with the forecast products abve three-day time level;b) There are some significant periods of day-to-day forecast skill of cases of T42L9 model according to the power spectrum analysis. The correlation analysis show that there are some EOF fields correlating with forecast skill of Northern Hemesphere at five-day time level. A simple barotropic quasi-geostrophic spectrum model is used to examine two typical case's barotropic instability. The results show that forecast skill is associated with the instability of initial field of the model and the allocation of error with background field of the cases.