Studying the long memory of financial time series can help people characterize financial markets accurately. However,studies on the interval financial time series are fewer. Therefore,the long-memory features of interval-based financial time series and its interval time series prediction model based on existing point-valued financial time series long memory modeling are considered in this paper. Firstly,the interval number is expressed as the interval center and the interval radius. Then,the center series and radius series are tested respectively whether they have long memory,and the interval-combination forecast model is proposed to predict the series which has long memory. Finally,an example about Shanghai Composite Index and Shenzhen Component Index is given to show that the interval stock index of Shanghai Composite Index has long memory,and the interval combination forecasting model can improve the prediction accuracy of interval financial time series.