The brain circuits and synaptic processes that underlie alcohol addiction are currently the subject of intensive research. Here we focus on hippocampal circuitry and show that chemogenetic inhibition of dentate gyrus (DG) during presentation of alcohol-associated cues has long-lasting effects on mice behavior. DG inhibition enhances alcohol seeking and drinking, suggesting that DG regulates addiction-related behaviors. To test this hypothesis, we perform whole-cell patch-clamp recordings from the granule cells of DG and look for electrophysiological correlates of alcohol addiction. We observe that presentation of alcohol-associated cue light that induces relapse to alcohol-seeking results in generation of silent synapses, that lack functional AMPA receptors. Furthermore, using human criteria of addiction, we differentiate mice controlling their alcohol consumption from those that undergo transition to addiction to discover that the levels of silent synapses induced by alcohol cues are specifically increased in the addicted mice. As the total level of dendritic spines that harbor synapses is constant at this time point, our data indicate that synapses of perforant path to DG are weakened during cue relapse. Finally we demonstrate that, acamprosate, a drug that limits alcohol drinking and seeking in addicts, prevents generation of silent synapses in DG upon presentation of alcohol-associated cues. Altogether, our data suggest that weakening of DG synapses upon cue relapse contributes to persistent alcohol addiction-related behaviors.