This paper presents a new approach to building an interval model for an industrial process with uncertainty that employs an interval neural network (INN), which can solve problems such as model structure demands and complexity limitations in the conventional unknown but bounded (UBB) errors method. A new architecture for an interval random vector functional-link network (IRVFLN) and its learning algorithm with penalty factors are proposed, to solve the problems such as the local minima, slow convergence, and very poor sensitivity to learning rate settings in the interval feed-forward neural networks with error back-propagation (IBPNNs). As an application case study, the IRVFLN is used to model the glutamic acid fermentation process under the condition of bounded-error data, and the test results indicate that the accuracy of the IRVFLN model meets the manufacturing requirements. The comparison is performed with IBPNN, and the results demonstrate that the proposed network outperforms IBPNN both on effectiveness and efficiency. Also, a comparison is given with a crisp (point-valued) approach using RVFLN, and the results show that the crisp approach is less reliable when existing uncertainties in measuring or process. (C) 2020 Elsevier Ltd. All rights reserved.