Accurate interval-valued stock price prediction is challenging and of great interest to investors and profit organizations. In this study, by considering individual stock information and relevant stock information simultaneously, we propose a novel interval dual convolutional neural network (Dual-CNNI) model method to predict interval-valued stock prices. First, the individual and relevant stock information are collected and transformed into images. Then, the Dual-CNNI model is proposed to predict interval-valued stock prices. Specifically, two convolutional neural network (CNN) models with different structures are constructed respectively extract individual stock features and relevant stock features, and then an interval multilayer perceptron (MLPI) model is used for final interval-valued stock price prediction. Finally, extensive experiments are conducted based on six randomly selected stocks, with comparison to several popular machine learning model based methods and interval-valued time series (ITS) prediction methods. The experimental results indicate that the proposed Dual-CNNI based method has superior predictive ability.