With the outbreak of COVID-19, medical imaging such as computed tomography (CT) based diagnosis is proved to be an effective way to fight against the rapid spread of the virus. Therefore, it is important to study computerized models for infectious detection based on CT imaging. New deep learning-based approaches are developed for CT assisted diagnosis of COVID-19. However, most of the current studies are based on a small size dataset of COVID-19 CT images as there are less publicly available datasets for patient privacy reasons. As a result, the performance of deep learning-based detection models needs to be improved based on a small size dataset. In this paper, a stacked autoencoder detector model is proposed to greatly improve the performance of the detection models such as precision rate and recall rate. Firstly, four autoencoders are constructed as the first four layers of the whole stacked autoencoder detector model being developed to extract better features of CT images. Secondly, the four autoencoders are cascaded together and connected to the dense layer and the softmax classifier to constitute the model. Finally, a new classification loss function is constructed by superimposing reconstruction loss to enhance the detection accuracy of the model. The experiment results show that our model is performed well on a small size COVID-2019 CT image dataset. Our model achieves the average accuracy, precision, recall, and F1-score rate of 94.7%, 96.54%, 94.1%, and 94.8%, respectively. The results reflect the ability of our model in discriminating COVID-19 images which might help radiologists in the diagnosis of suspected COVID-19 patients.