Genetic conflict between viruses and their hosts drives evolution and genetic innovation. Prokaryotes evolved CRISPR-mediated adaptive immune systems for protection from viral infection, and viruses have evolved diverse anti-CRISPR (Acr) proteins that subvert these immune systems. The adaptive immune system in Pseudomonas aeruginosa (type I-F) relies on a 350 kDa CRISPR RNA (crRNA)-guided surveillance complex (Csy complex) to bind foreign DNA and recruit a trans-acting nuclease for target degradation. Here, we report the cryo-electron microscopy (cryo-EM) structure of the Csy complex bound to two different Acr proteins, AcrF1 and AcrF2, at an average resolution of 3.4 Å. The structure explains the molecular mechanism for immune system suppression, and structure-guided mutations show that the Acr proteins bind to residues essential for crRNA-mediated detection of DNA. Collectively, these data provide a snapshot of an ongoing molecular arms race between viral suppressors and the immune system they target. Display omitted •Cryo-EM structure of crRNA-guided surveillance complex bound to two anti-CRISPRs•Anti-CRISPRs bind to residues that are essential for crRNA-guided DNA binding•Cas7f backbone subunits have unique fold, suggesting a unique evolutionary trajectory•AcrF2 is a molecular mimic of double-stranded DNA The high-resolution structures of a CRISPR surveillance complex with two viral anti-CRISPR proteins reveal different strategies for silencing CRISPR immune function.