The COVID-19 pandemic is caused by SARS-CoV-2 infection. Human angiotensin-converting enzyme II (hACE2) has been identified as the receptor enabling SARS-CoV-2 host entry. To establish a mouse model for COVID-19, we generated transgenic mouse lines using the (HS4)2-pCAG-hACE2-HA-(HS4)2 transgene cassette, which expresses HA-tagged hACE2 under control of the CAG promoter and is flanked by HS4 insulators. Expression levels of the hACE2 transgene are respectively higher in lung, brain and kidney of our CAG-hACE2 transgenic mice and relatively lower in duodenum, heart and liver. The CAG-hACE2 mice are highly susceptibility to SARS-CoV-2 infection, with 100 PFU of SARS-CoV-2 being sufficient to induce 87.5% mortality at 9 days post-infection and resulting in a sole (female) survivor. Mortality was 100% at the higher titer of 1000 PFU. At lower viral titers, we also found that female mice exposed to SARS-CoV-2 infection suffered much less weight loss than male mice, implying sex-biased responses to SARS-CoV-2 infection. We subjected neuronal cultures to SARS-CoV-2 pseudovirus infection to ascertain the susceptibilities of neurons and astrocytes. Moreover, we observed that expression of SARS-CoV-2 Spike protein alters the synaptic responses of cultured neurons. Our transgenic mice may serve as a model for severe COVID-19 and sex-biased responses to SARS-CoV-2 infection, aiding in the development of vaccines and therapeutic treatments for this disease.