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In view of the intrinsic complexity of the oil market, crude oil prices are influenced by numerous factors that make forecasting very difficult. Recognizing this challenge, numerous approaches have been introduced, but little work has been done concerning the interval-valued prices. To capture the underlying characteristics of crude oil price movements, this paper proposes a two-stage forecasting procedure to forecast interval-valued time series, which generalizes point-valued forecasts to incorporate uncertainty and variability. The empirical results show that our proposed approach significantly outperforms all the benchmark models in terms of both forecasting accuracy and robustness analysis. These results can provide references for decision-makers to understand the trends of crude oil prices and improve the efficiency of economic activities.