Alcohol use disorders and anxiety disorders are highly comorbid in humans. In rodent lines selected for alcohol drinking, differences in anxiety-like behavior are also seen. The High Drinking in the Dark (HDID) lines of mice are selectively bred for drinking to intoxication during limited access to alcohol, and these mice represent a genetic model of risk for binge-like drinking. The present studies investigated whether these selected lines differ from control (HS) mice in basal anxiety behavior or in anxiolytic response to alcohol. We also assessed the genetic correlation between alcohol drinking in the dark (DID) and basal anxiety-like behavior using existing inbred strain data. Mice of both sexes and HDID replicates (HDID-1 and HDID-2) were tested on an elevated zero maze immediately following a DID test. In general, HDID mice showed more time spent in the open arms after drinking alcohol than HS mice, and open-arm time was significantly correlated with blood alcohol concentration. HDID-1 male mice also showed less anxiety-like behavior at baseline (water-drinking controls). In a separate experiment, HDID-1 and HS mice were tested for anxiolytic dose-response to acute alcohol injections. Both genotypes showed increasing time spent in the open arms with increasing alcohol doses, and HDID-1 and female mice had greater open-arm time across all doses. HDID-1 control males showed lower anxiety-like behavior than the HS control males. Inbred strain data analysis also showed no significant genetic relationship between alcohol DID and anxiety. These findings suggest that HDID selection has not produced systematic changes in anxiety-like behavior or sensitivity to alcohol-induced anxiolysis, though there is a tendency in the male mice of the first replicate toward reduced basal anxiety-like behavior. Therefore, anxiety state and sensitivity to alcohol's anxiolytic effects do not appear to contribute significantly to the high drinking behavior of the HDID mice.