Background: The COVID-19 pandemic led to a change in work organization with the development of telework. The purpose of this study was to assess the prevalence of anxiety and depressive symptoms in teleworking staff in a university hospital center in France during the first lockdown, and to identify personal, medical and occupational factors associated with anxiety disorder. Methods: A cross-sectional observational study was conducted in 474 hospital staff working from home during the first lockdown. The sociodemographic, occupational and medical information (anxiety and depressive disorders measured on the Hospital Anxiety and Depression (HAD) scale) was collected by an anonymous online self-administered questionnaire. The variables associated with anxiety disorder were investigated by a univariate analysis (chi² and Fisher tests) and a multivariate analysis (logistic regression model). Results: Three hundred and forty hospital staff participated in the study (72% response rate). Of the participants, 106 subjects (32.1%) showed signs of an anxiety disorder and 26 (7.65%) of a depressive disorder. An anxiety disorder was significantly associated with mental workload, changes in working hours, difficulties in teleworking due to issues of internet connection or due to noise, difficulties in combining family and occupational life, sleep disturbance, worry about media information and worry about the health of a loved one. An anxiety disorder remained associated with occupational stress and personal stress during lockdown after a multivariate logistic regression. Conclusions: This study highlighted the association between an anxiety disorder and perceived occupational and personal stress levels in hospital staff teleworking during the first lockdown. Stress management workshops could be proposed to hospital staff. Prevention of anxiety requires reinforced medical monitoring and reduced stress.