The highly contagious and rapidly mutating COVID-19 virus is affecting individuals worldwide. A rapid and large-scale method for COVID-19 testing is needed to prevent infection. Cough testing using AI has been shown to be potentially valuable. In this paper, we propose a COVID-19 diagnostic method based on an AI cough test. We used only crowdsourced cough sound data to distinguish between the cough sound of COVID-19-positive people and that of healthy people. First, we used the COUGHVID cough database to segment only the cough sound from the original cough data. An effective audio feature set was then extracted from the segmented cough sounds. A deep learning model was trained on the extracted feature set. The COVID-19 diagnostic system constructed using this method had a sensitivity of 93% and a specificity of 94%, and achieved better results than models trained by other existing methods.