Chest computed tomography (CT) has played an essential diagnostic role in assessing patients with COVID-19 by showing disease-specific image features such as ground-glass opacity and consolidation. Image segmentation methods have proven to help quantify the disease burden and even help predict the outcome. The availability of longitudinal CT series may also result in an efficient and effective method to reliably assess the progression of COVID-19, monitor the healing process and the response to different therapeutic strategies. In this paper, we propose a new framework to identify infection at a voxel level (identification of healthy lung, consolidation, and ground-glass opacity) and visualize the progression of COVID-19 using sequential low-dose non-contrast CT scans. In particular, we devise a longitudinal segmentation network that utilizes the reference scan information to improve the performance of disease identification. Experimental results on a clinical longitudinal dataset collected in our institution show the effectiveness of the proposed method compared to the static deep neural networks for disease quantification.