Severe acute respiratory syndrome coronavirus 2 infection causing coronavirus disease 2019 has spread worldwide. Whether antibodies are important for the adaptive immune responses against SARS-CoV-2 infection needs to be determined. Here, 26 cases of COVID-19 in Jinan, China, were examined and shown to be mild or with common clinical symptoms and no cases of severe symptoms were found among these patients. A striking feature of some patients is that SARS-CoV-2 could exist in patients who have virus-specific IgG antibodies for a very long period, with one case for up to 36 days. One COVID-19 patient who did not produce any SARS-CoV-2-bound IgG successfully cleared SARS-CoV-2 after 46 days of illness, revealing that without antibody-mediated adaptive immunity, innate immunity may still be powerful enough to eliminate SARS-CoV-2. Overall, this report may provide a basis for further analysis of both innate and adaptive immunity in SARS-CoV-2 clearance, especially in non-severe cases. This study also has implications for understanding the pathogenesis and treatment of SARS-CoV-2.