SARS-CoV-2 pandemic is causing high morbidity and mortality burden worldwide with unprecedented strain on health care systems. To investigate the time course of the antibody response in relation to the outcome we performed a study in hospitalized COVID-19 patients. As comparison we also investigated the time course of the antibody response in SARS-CoV-2 asymptomatic subjects. Study results show that patients produce a strong antibody response to SARS-CoV-2 with high correlation between different viral antigens (spike protein and nucleoprotein) and among antibody classes (IgA, IgG, and IgM and neutralizing antibodies). The antibody peak is reached by 3 weeks from hospital admission followed by a sharp decrease. No difference was observed in any parameter of the antibody classes, including neutralizing antibodies, between subjects who recovered or with fatal outcome. Only few asymptomatic subjects developed antibodies at detectable levels.