Bacteriophages encode anti-CRISPR suppressors to counteract the CRISPR/Cas immunity of their bacterial hosts, thus facilitating their survival and replication. Previous studies have shown that two phage-encoded anti-CRISPR proteins, AcrF1 and AcrF2, suppress the type I-F CRISPR/Cas system of Pseudomonas aeruginosa by preventing target DNA recognition by the Csy surveillance complex, but the precise underlying mechanism was unknown. Here we present the structure of AcrF1/2 bound to the Csy complex determined by cryo-EM single-particle reconstruction. By structural analysis, we found that AcrF1 inhibits target DNA recognition of the Csy complex by interfering with base pairing between the DNA target strand and crRNA spacer. In addition, multiple copies of AcrF1 bind to the Csy complex with different modes when working individually or cooperating with AcrF2, which might exclude target DNA binding through different mechanisms. Together with previous reports, we provide a comprehensive working scenario for the two anti-CRISPR suppressors, AcrF1 and AcrF2, which silence CRISPR/Cas immunity by targeting the Csy surveillance complex.