For the time series with obvious seasonal characteristics, first, the seasonal fluctuations are taken off by application of moving average method in order to get a smooth time sequence, then grey GM(1, 1) differential equation is set up to further derive self-memory forecast model of time series. When the model is applied to fitting and forecasting of the actual observation time series, the results show that the forecast model about seasonal time series put forward in this paper not only reflects the time series’ inter-annual general variation trend, but also can do validated forecast for the fluctuation characteristics and extreme value condition in each month of one year.