Currently, COVID-19 is spreading all over the world and profoundly impacting people's lives and economic activities. In this paper, a novel approach called the COVID-19 Quantum Neural Network (CQNN) for predicting the severity of COVID-19 in patients is proposed. It consists of two phases: In the first, the most distinct subset of features in a dataset is identified using a Quick Reduct Feature Selection (QRFS) method to improve its classification performance; and, in the second, machine learning is used to train the quantum neural network to classify the risk. It is found that patients' serial blood counts (their numbers of lymphocytes from days 1 to 15 after admission to hospital) are associated with relapse rates and evaluations of COVID-19 infections. Accordingly, the severity of COVID- 19 is classified in two categories, serious and non-serious. The experimental results indicate that the proposed CQNN's prediction approach outperforms those of other classification algorithms and its high accuracy confirms its effectiveness.