In light of the coronavirus disease 2019 (COVID-19) pandemic and the enormous amount of uncertainty caused by it, mental health issues have become a great concern. Evidence regarding the effects of psychological resilience on the Thai population is scarce. We evaluated psychological resilience during the first wave of the COVID-19 pandemic and its association with the risk of mental health outcomes, such as depression, anxiety, stress, and health-related well-being. This cross-sectional study was a part of the HOME-COVID-19 project, which conducted an online survey of 4004 members of the general population in Thailand using the Brief Resilience Coping Scale. Logistic regression was performed to identify the association between psychological resilience and mental health issues and well-being. Groups with prevalence rates of 43.9%, 39.2%, and 16.9% were classified as low, moderate, and high resilient copers, respectively. Using high resilient copers as a reference group, the low resilient copers had a higher chance of having mental health adversities. The adjusted odds ratio (OR) was 1.89 (95% confidence interval [CI], 1.39–2.56; p < 0.001) for depression, 2.13 (95% CI, 1.45–3.14; p < 0.001) for anxiety, 4.61 (95% CI, 3.30–6.45; p < 0.001) for perceived stress, and 3.18 (95% CI, 2.31–4.38; p < 0.001) for low well-being. For the medium resilient copers, only low well-being was found to be statistically significant (OR, 1.60; 95% CI, 1.16–2.20; p = 0.004). It is important that resilience be considered in the development of strategies for managing the COVID-19 pandemic to prevent or reduce adverse mental health outcomes.