Severe Acute Respiratory Syndrome Coronavirus -2 (SARS-CoV-2) emerged in late 2019 and has spread worldwide resulting in the Coronavirus Disease 2019 (COVID-19) pandemic. Although animal models have been evaluated for SARS-CoV-2 infection, none have recapitulated the severe lung disease phenotypes seen in hospitalized human cases. Here, we evaluate heterozygous transgenic mice expressing the human ACE2 receptor driven by the epithelial cell cytokeratin-18 gene promoter (K18-hACE2) as a model of SARS-CoV-2 infection. Intranasal inoculation of SARS-CoV-2 in K18-hACE2 mice results in high levels of viral infection in lung tissues with additional spread to other organs. Remarkably, a decline in pulmonary function, as measured by static and dynamic tests of respiratory capacity, occurs 4 days after peak viral titer and correlates with an inflammatory response marked by infiltration into the lung of monocytes, neutrophils, and activated T cells resulting in pneumonia. Cytokine profiling and RNA sequencing analysis of SARS-CoV-2-infected lung tissues show a massively upregulated innate immune response with prominent signatures of NF-kB-dependent, type I and II interferon signaling, and leukocyte activation pathways. Thus, the K18-hACE2 model of SARS-CoV-2 infection recapitulates many features of severe COVID-19 infection in humans and can be used to define the mechanistic basis of lung disease and test immune and antiviral-based countermeasures.