Crude oil is the most important energy source in the world, and fluctuations in oil prices can significantly influence investors, companies, and governments. However, crude oil prices have numerous characteristics, including randomness, sudden structural changes, intrinsic nonlinearity, volatility, and chaotic nature. This makes the accurate forecasting of crude oil prices a difficult and challenging task. In this paper, a hybrid prediction model for crude oil futures prices is proposed, the accuracy and robustness of which are demonstrated via controlled experiments and sensitivity analysis. This study uses a new data denoising method for data processing to improve the accuracy and stability of the predictions of crude oil prices. Furthermore, the chaotic time-series prediction method, shallow neural networks, linear model prediction methods, and deep learning methods are adopted as submodels. The results of interval forecasts with narrow widths and high prediction accuracies are derived by introducing a confidence interval adjustment coefficient. The results of the simulation experiments indicate that the proposed hybrid prediction model exhibits higher accuracy and efficiency, as well as better robustness of the forecasting than the control models. In summary, the proposed forecasting framework can derive accurate point and interval forecasts and provide a valuable reference for the price forecasting of crude oil futures.