Attribute reduction is an important part of knowledge acquisition. At present, the research on attribute reduction of the interval rough number information system is very scarce. Firstly, considering the existence of redundancy in the classification results of existing researches and the fact that the classification redundancy is not yet measured, the concept of coverage classification redundancy is proposed in the interval rough number information system. After similar class and beta-maximal consistent class are proposed, the concept of beta-equivalent class is proposed, so that the result of classifying the domain by beta-equivalent class is a division of the domain, and the coverage classification redundancy decrease to 0. On this basis, an attribute reduction definition which keeps the beta-equivalent class invariant is proposed for the interval rough number information system. At the same time, according to the characteristics of the beta-equivalent class, an attribute reduction method is given, which only uses an element in the beta-equivalent class as a distinguishing object to establish the distinguishing matrices. Finally, examples are given to illustrate the effectiveness of the proposed method.