In recent years, COVID-19 has spread rapidly among humans. Chest CT is an effective means of diagnosing COVID-19. However, the diagnosis of CT images still depends on the doctor's visual judgment and medical experience. This takes a certain amount of time and may lead to misjudgment. In this paper, a new algorithm for automatic diagnosis of COVID-19 based on chest CT image data was proposed. The algorithm comprehensively uses WE to extract image features, uses ELM for training, and finally passes k-fold CV validation. After evaluating and detecting performance on 296 chest CT images, our proposed method is superior to state-of-the-art approaches in terms of sensitivity, specificity, precision, accuracy, F1, MCC and FMI.