Background: Few studies in Nigeria have investigated the relationship between psychiatric morbidity and alcohol use. Fewer still have specifically examined problem drinking and mental well-being among students. Yet, available evidence worldwide suggests that alcohol related problems might be a major problem among students. Aim: The aim of this study was to examine the relationship between alcohol use and psychological well being among undergraduates of a Nigerian tertiary institution. The objectives included determining the prevalence and pattern of problematic alcohol use and ascertaining the association between alcohol use and some socio-demographic variables. Method: The Alcohol Use Disorders Identification Test (AUDIT) was used to evaluate for alcohol related problems in 443 students. A questionnaire was also used to elicit Sociodemographic variables while psychological well-being was assessed with the General Health Questionnaire (GHQ-28). Results: One year prevalence of alcohol use was 40.6% while alcohol related problems were found in 14.9% of the students using the AUDIT questionnaire with a cut-off score of 5. Heavy episodic alcohol use was reported by 31.1% while alcohol related injury had occurred among 8.9% of the students. Factors significantly associated with alcohol consumption were male sex (2 = 24.43; p< 0.01), non-religiosity (2 = 55.12; p<0.01) and type of religion (2 = 8.92; p<0.05). Male gender (2 = 4.54p<0.05), older age (2 = 3.92; p<0.05) and higher paternal education (2 = 4.40; p<0.05) were associated with problem drinking. The prevalence of psychological distress (GHQ ≥ 5) was 13.8%. Psychological distress was significantly associated with parent-child relationship Father (2 = 4.78; p<0.05); Mother (2 = 3.24; p<0.05) among students that drank alcohol. Also, psychological distress was significantly associated with heavy episodic drinking (2 = 9.58; p<0.05), history of alcohol related injury (2 = 3.96; p<0.05), and alcohol dependence (2 = 13.2; p<0.001). Conclusion: Alcohol related problems were found among students of the tertiary institution. This may have important psychosocial implications. Mental health is a critical component of alcohol abuse and dependence prevention programmes.