SARS-CoV-2 is the etiologic agent of COVID-19, which has led to a dramatic loss of human life and presents an unprecedented challenge to public health worldwide. The gold standard assay for SARS-CoV-2 identification is real-time polymerase chain reaction; however, this assay depends on highly trained personnel and sophisticated equipment and may suffer from false results. Thus, a serological antibody test is a supplement to the diagnosis or screening of SARS-CoV-2. Here, we develop and evaluate the diagnostic performance of an IgM/IgG indirect ELISA method for antibodies against SARS-CoV-2 in COVID-19. The ELISA was constructed by coating with a recombinant nucleocapsid protein of SARS-CoV-2 on an enzyme immunoassay plate, and its sensitivity and specificity for clinical diagnosis of SARS-CoV-2 infection was assessed by detecting the SARS-CoV-2-specific IgM and IgG antibodies in COVID-19 patient’s sera or healthy person’s sera. The SARS-CoV-2 positive serum samples (n = 168) were collected from confirmed COVID-19 patients. A commercial nucleocapsid protein-based chemiluminescent immunoassay (CLIA) kit and a colloidal gold immunochromatography kit were compared with those of the ELISA assay. The specificity, sensitivity, positive predictive value (PPV), and negative predictive value (NPV) of IgM were 100, 95.24, 100, and 91.84%, whereas those of IgG were 100, 97.02, 100, and 94.74%, respectively. We developed a highly sensitive and specific SARS-CoV-2 nucleocapsid protein-based ELISA method for the diagnosis and epidemiologic investigation of COVID-19 by SARS-CoV-2 IgM and IgG antibody detection.