The purpose of this study is to examine the association of anxiety with self-rated general health, satisfaction with life, stress and coping strategies of university students during the COVID-19 pandemic outbreak in Poland. Participants and Methods: A total of 914 university students, ranged in age between 18 and 40 years old (M = 23.04, SD = 2.60), participated in an online survey. The study was performed between 30 March and 30 April 2020, during the general coronavirus quarantine. Participants completed a standard psychological questionnaire, including General Anxiety Disorder (GAD-7), General Self-Rated Health (GSRH), Satisfaction With Life Scale (SWLS), Perceived Stress Scale (PSS), and Coping Inventory for Stressful Situations (CISS). Results: The majority of students (65%) showed mild to severe GAD and a high level of perceived stress (56%). Those students who had the worst evaluated current GSRH, in comparison to the situation before the COVID-19 outbreak, also demonstrated higher levels of anxiety, perceived stress, and emotion-oriented coping styles. The study indicates that the variance of anxiety during the COVID-19 outbreak may be explained for about 60% by such variables, like high stress, low general self-rated health, female gender, and frequent use of both emotion-oriented and task-oriented coping styles. Conclusion: University students experience extremely high stress and anxiety during quarantine period and they need professional help to cope with COVID-19 pandemic. The results of this study may help prepare appropriate future intervention and effective prevention programs at universities.