This paper has proposed an effective intelligent prediction model that can well discriminate and specify the severity of Coronavirus Disease 2019 (COVID-19) infection in clinical diagnosis and provide a criterion for clinicians to weigh scientific and rational medical decision-making. With indicators as the age and gender of the patients and 26 blood routine indexes, a severity prediction framework for COVID-19 is proposed based on machine learning techniques. The framework consists mainly of a random forest and a support vector machine (SVM) model optimized by a slime mould algorithm (SMA). When the random forest was used to identify the key factors, SMA was employed to train an optimal SVM model. Based on the COVID-19 data, comparative experiments were conducted between RF-SMA-SVM and several well-known machine learning algorithms performed. The results indicate that the proposed RF-SMA-SVM not only achieves better classification performance and higher stability on four metrics, but also screens out the main factors that distinguish severe COVID-19 patients from non-severe ones. Therefore, there is a conclusion that the RF-SMA-SVM model can provide an effective auxiliary diagnosis scheme for the clinical diagnosis of COVID-19 infection.