Crude oil price volatility prediction are important for energy policymaking and investment risk avoidance, and have attracted a great deal of global attention. In recent years, although some studies have proposed methods for prediction crude oil price volatility, most of them are point prediction, which are difficult to provide richer reference information for managers. Therefore, an improved hybrid interval prediction model is proposed. The hybrid model combines data feature extraction and quantification techniques, fuzzy information granulation(FIG), improved echo state network (IESN), and autoregressive integrated moving average model (ARIMA). The hybrid model is able to accurately portray the different features present in the volatility of crude oil spot price. The features are quantified in order to merge similar feature components and improve the prediction effect. On this basis, IESN, which possesses strong nonlinear learning ability, is used to predict high-frequency sequences, and ARIMA, which has strong linear carving ability, is used to predict low-frequency sequences and residual terms. By “divide and conquer”, excellent prediction intervals are obtained. West Texas intermediate (WTI) crude oil spot and Brent crude oil spot are selected for analysis, and consider the influence of futures on interval construction. The effect of volatility intervals is validated from the pricing benchmark and time scale dimensions, respectively. The experimental results show that the proposed model has optimal performance in all scenarios. Take the performance of WTI on the daily scale as an example, its PICWC value is 0.8205. Compared with other benchmark models, it improves by 137.4504, 3.1118, 1.0506, and 0.4875, respectively. The proposed model provides a reliable new idea for crude oil spot volatility interval prediction.