Quarantine situations have deleterious effects on the mental health of the general population, but it is expected that LGBTQ (lesbian, gay, bisexual, transgender, and queer) individuals are even more affected. We aimed to investigate the extent to which the psychosocial effects of the COVID-19 pandemic are associated with changes in the mental health of LGBTQ adolescents and young adults (N = 403). The findings indicated that (i) not having or entered into a university degree, (ii) the daily negative impact of the pandemic, and (iii) a negative family climate were associated with higher levels of depression and anxiety. Furthermore, family climate partially mediated the association between the pandemic's individual impact and both depression and anxiety. Organizations promoting the rights of LGBTQ individuals, health and educational services, and other support networks, should remain available to meet the needs of this population.