Recent studies have revealed that N7-methylguanosine(m7G) plays a pivotal role in various biological processes and disease pathogenesis. To date, transcriptome-wide m7G modification sites have been identified by high-throughput sequencing approaches, and some related information has been recorded in a few biological databases. However, the mechanism of site action in disease remains uncharted. Wet experiments can help identify true m7G sites with high confidence, but it is time-consuming to find the true ones in such a large number of sites, which will also cost too much. Thus, computational methods are emergently needed to predict the associations between m7G sites and various diseases, thus help to uncover potential active sites for specific diseases. In this article, we proposed a bounded robust principal component analysis (BRPCA) method to predict unknown m7G-disease association based on similarity information. Importantly, BRPCA tolerates the noise and redundancy existing in association and similarity information. Moreover, a suitable bounded constraint is incorporated into BRPCA to ensure that the predicted association scores locate in a meaningful interval. The extensive experiments demonstrate the superiority and robustness of the BRPCA.