This paper presents data on the initial impacts of COVID-19 on psychological distress among the Australian population and compares these data to a nationally representative sample in the United States. The Australian survey is based on interviews with 3,155 Australians over the period 14-27 April 2020, with many of these respondents linked at the individual level to survey responses obtained prior to the spread of COVID-19. We find a substantial increase in the levels of psychological distress between February 2017 and April 2020 for the Australian population, increasing from 8.4 per cent reporting a serious mental illness in 2017 to 10.6 per cent during the COVID-19 pandemic. These increases in severe psychological distress are largely concentrated in young Australian adults aged 18 to 34 years. Compared to the survey in the United States of over 10,000 respondents, Australia does not appear to have as high levels of distress on average. However, the levels of psychological distress reported by younger Australian adults are similar to those being reported by Americans of the same age. While a substantial minority of Australians are experiencing higher rates of psychological distress as a result of the COVID-19 pandemic, there were some positive findings. In Australia, 61 per cent of people were very hopeful about the future, higher than the rate in the US of 52 per cent. These high levels of hope for the future were also found to be protective against some of the negative mental health impacts during this time.