We explored heritabilities of the State and Trait Anxiety Inventory (STAI) and the Alcohol Use Disorders Identification Test (AUDIT), and associations including genetic and environmental correlations between the phenotypes among Korean twins and their families. We analyzed the data of 1,748 participants (835 men, 913 women, 656 individuals of monozygotic twins, 173 individuals of same-sexed dizygotic twins, 919 non-twin family members, age 30–79 years) from the Healthy Twin study. Heritabilities and bivariate analyses were assessed using the SOLAR package software. In the methods of generalized estimation equations, women in the 4th quartile of state and trait scores were 17% and 15%, respectively more likely to be hazardous alcohol users compared to women in the lower three quartiles (P < .05). However, there were no significant associations between these phenotypes in men. After adjusting for age and squared age, the heritability estimates were 0.26 in men and 0.34 in women for the state score; for the trait score, 0.35 in men and 0.31 in women; for the AUDIT score, 0.32 in men and 0.37 in women (P < .001). After adjusting for age and squared age, there was a significant genetic correlation between the trait score and the AUDIT score, and a significant non-genetic correlation between the state score and the AUDIT score in women, while there were no significant genetic or non-genetic correlations between these phenotypes in men. The STAI and AUDIT scores are heritable in Koreans and the relationships between these phenotypes may be inconsistent by sex.