This paper proposes an interval-based methodology to model and forecast the price range or range-based volatility process of financial asset prices. Comparing with the existing volatility models, the proposed model utilizes more information contained in the interval time series than using the range information only or modeling the high and low price processes separately. An empirical study of the U.S. stock market daily data shows that the proposed interval-based model produces more accurate range forecasts than the classic point-based linear models for range process, in terms of both in-sample and out-of-sample forecasts. The statistical tests show that the forecasting advantages of the interval-based model are statistically significant in most cases. In addition, some stability tests have been conducted for ascertaining the advantages of the interval-based model through different sample windows and forecasting periods, which reveals similar results. This study provides a new interval-based perspective for volatility modeling and forecasting of financial time series data.