To defend against the invasion of phages, most Archaea and bacteria possess the adaptive immune systems, which are formed by clustered regularly interspaced short palindromic repeats (CRISPR) and CRISPR-associated (Cas) proteins. To counteract the CRISPR-Cas systems, phages express anti-CRISPR (Acr) proteins to inhibit CRISPR-dependent response. AcrVA2 from Moraxella bovoculi is an inhibitor of Type V-A CRISPR-Cas system. However, the structure and inhibition mechanism of AcrVA2 remain to be elucidated. Here we report the crystal structures of AcrVA2 in the apo state and MbCas12a^620-636-AcrVA2 complex. AcrVA2 adopts a novel α-β fold and binds to MbCas12a in free state. The structure of MbCas12a^620-636-AcrVA2 complex reveals that AcrVA2 interacts with MbCas12a via hydrogen bonds and salt bridges, as well as hydrophobic interaction. These results suggest that AcrVA2 affect the activity of Cas12a by binding to the MbCas12a in the apo state. These results provide significant insights into the mechanism of AcrVA2 disabling Type V-A CRISPR-Cas system.