Cas13 has demonstrated unique and broad utility in RNA editing, nucleic acid detection, and disease diagnosis; however, a constantly active Cas enzyme may induce unwanted effects. Bacteriophage- or prophage-region-encoded anti-CRISPR (acr) gene molecules provide the potential to control targeting specificity and potency to allow for optimal RNA editing and nucleic acid detection by spatiotemporally modulating endonuclease activities. Using integrated approaches to screen acrVI candidates and evaluate their effects on Cas13 function, we discovered a series of acrVIA1-7 genes that block the activities of Cas13a. These VI-A CRISPR inhibitors substantially attenuate RNA targeting and editing by Cas13a in human cells. Strikingly, type VI-A anti-CRISPRs (AcrVIAs) also significantly muffle the single-nucleic-acid editing ability of the dCas13a RNA-editing system. Mechanistically, AcrVIA1, -4, -5, and -6 bind LwaCas13a, while AcrVIA2 and -3 can only bind the LwaCas13-crRNA (CRISPR RNA) complex. These identified acr molecules may enable precise RNA editing in Cas13-based application and study of phage-bacterium interaction.