The psychological well-being of students may be especially affected by the COVID-19 pandemic; international students can lack local support systems and represent a higher risk subgroup. Self-reported depressive symptoms, suicidal ideation, anxiety, post-traumatic stress disorder (PTSD), insomnia, alcohol use, academic stress, and loneliness were examined in two cohorts of university students (March 2020 n = 207, March 2021 n = 142). We investigated differences i) between 2020 and 2021, ii) between domestic and international students, and ii) whether differences between the two cohorts were moderated by student status. More depressive symptoms, academic stress, and loneliness were reported in 2021. International students reported more depressive symptoms, suicidal ideation, anxiety, PTSD, academic stress, and loneliness. The main effect of cohort was not moderated by student status. Conclusions: International students had worse mental health outcomes overall, but were not affected more by the COVID-19 pandemic than domestic students.