Objective: The study aimed to assess anxiety and fear of COVID-19 among home-staying Bangladeshi students. Participants: A total of 3997 university students across Bangladesh participated in the study. Methods: A cross-sectional study was conducted using the generalized anxiety disorder scale and the fear of COVID-19 scale to measure anxiety and fear, respectively. Results: 40.11% of participants had anxiety. Fear of death by COVID-19 ([Beta]1'=4.45; 95% CI: 3.99-4.90) and perceiving COVID-19-like symptoms as having COVID-19 ([Beta]1'=2.47; 95% CI: 1.76-3.18) were associated with higher fear. Exposure to COVID-19 news on social media was a predictor of fear and anxiety. Furthermore, the severe educational loss was associated with fear ([Beta]1'=2.88; 95% CI: 2.25-3.50) and anxiety ([Beta]2'=1.91; 95% CI: 1.41 to 2.41). Physical exercise and recreational activities were protective factors for fear and anxiety. Conclusion: The study reports a higher level of psychological difficulties among students during the COVID-19 pandemic which needs further longitudinal exploration to design appropriate interventions.