Individuals are different in a relatively constant pattern of thoughts, feeling, and behaviors, which are called personality traits. Mental health is a condition of well-being in which people may reach their full potential and deal effectively with stress, work efficiently, and contribute to their communities. Indeed, the link between personality and mental health as indicated by the 12-item version of the general health questionnaires (GHQ-12) has been well-established according to evidence found by decades of research. However, the GHQ-12 comprises many questions asking about different dimensions of mental health. It is unclear how personality traits relate to these dimensions of mental health. In this paper, we try to address this question. We analyzed data from 12,007 participants from the British Household Panel Study (BHPS) using a confirmatory factor analysis (CFA) and generalized linear models. We replicated the factor structure of GHQ-12 labeled as GHQ-12A (social dysfunction & anhedonia; 6 items), GHQ-12B (depression & anxiety; 4 items), and GHQ-12C (loss of confidence; 2 items). Moreover, Neuroticism was positively related to all dimensions of mental health issues, Extraversion was negatively related to GHQ-12A (social dysfunction & anhedonia) and GHQ-12B (depression & anxiety), Agreeableness and Conscientiousness were negatively related to GHQ-12A (social dysfunction & anhedonia) and GHQ-12C (loss of confidence), and Openness was negatively related to GHQ-12B (depression & anxiety). These results contribute to theories including the predisposition/vulnerability model, complication/scar model, pathoplasty/exacerbation model, and the spectrum model, which propose that personality traits are linked to mental health and explained possible reasons. Psychologists may use results from this study to identify individuals who may be at high risk of developing various non-psychiatric mental health issues and intervene to avoid negative outcomes.