Borna disease virus (BoDV-1) is a bornavirus that infects the central nervous systems of various animal species, including humans, and causes fatal encephalitis. BoDV-1 also establishes persistent infection in neuronal cells and causes neurobehavioral abnormalities. Once neuronal cells or normal neural networks are lost by BoDV-1 infection, it is difficult to regenerate damaged neural networks. Therefore, the development of efficient anti-BoDV-1 treatments is important to improve the outcomes of the infection. Recently, one of the clustered regularly interspaced short palindromic repeats (CRISPRs) and CRISPR-associated (Cas) systems, CRISPR/Cas13, has been utilized as antiviral tools. However, it is still unrevealed whether the CRISPR/Cas13 system can suppress RNA viruses in persistently infected cells. In this study, we addressed this question using persistently BoDV-1-infected cells. The CRISPR/Cas13 system targeting viral mRNAs efficiently decreased the levels of target viral mRNAs and genomic RNA (gRNA) in persistently infected cells. Furthermore, the CRISPR/Cas13 system targeting viral mRNAs also suppressed BoDV-1 infection if the system was introduced prior to the infection. Collectively, we demonstrated that the CRISPR/Cas13 system can suppress BoDV-1 in both acute and persistent infections. Our findings will open the avenue to treat prolonged infection with RNA viruses using the CRISPR/Cas13 system.