Food insecurity is an ongoing public health issue and contributes to mental health status. We investigated whether food insecurity is associated with inadequate nutrient intake and whether it affects mental health indicators (perceived stress/experience of depressive symptom/suicidal ideation) and quality of life (QOL) among Koreans (n = 5862, 20–64 years) using data from the Korea National Health and Nutritional Examination Survey (2012–2013). Household food security status was categorized as “food-secure household”, “food-insecure household without hunger”, and “food-insecure household with hunger”. Data on food insecurity, sociodemographic factors, nutrient intake, mental health indicators, and QOL were used. A logistic regression model was conducted to determine odds ratios (ORs) for psychological health. A greater proportion of food-insecure participants were nutritionally deficient compared with expectations of the 2015 Korean Dietary Reference Intakes. These deficiencies were generally higher in both “food-insecure household” groups. Both “food-insecure household” groups, particularly the “food-insecure household with hunger” group showed significantly adverse mental health status (ORs: 1.52–3.83) and lower QOL (ORs: 1.49–3.92) than did the “food-secure household” group before and after adjusting for sex, age, education, household income, smoking/alcohol consumption, physical activity, marital status, and receiving food assistance. In conclusion, food insecurity may be significantly associated with adverse mental health indicators and decreased QOL in young/middle-aged Koreans.