Blur is a key property in the perception of COVID-19 computed tomography (CT) image manifestations. Typically, blur causes edge extension, which brings shape changes in infection regions. Tchebichef moments (TM) have been verified efficiently in shape representation. Intuitively, disease progression of same patient over time during the treatment is represented as different blur degrees of infection regions, since different blur degrees cause the magnitudes change of TM on infection regions image, blur of infection regions can be captured by TM. With the above observation, a longitudinal objective quantitative evaluation method for COVID-19 disease progression based on TM is proposed. COVID-19 disease progression CT image database (COVID-19 DPID) is built to employ radiologist subjective ratings and manual contouring, which can test and compare disease progression on the CT images acquired from the same patient over time. Then the images are preprocessed, including lung automatic segmentation, longitudinal registration, slice fusion, and a fused slice image with region of interest (ROI) is obtained. Next, the gradient of a fused ROI image is calculated to represent the shape. The gradient image of fused ROI is separated into same size blocks, a block energy is calculated as quadratic sum of non-direct current moment values. Finally, the objective assessment score is obtained by TM energy-normalized applying block variances. We have conducted experiment on COVID-19 DPID and the experiment results indicate that our proposed metric supplies a satisfactory correlation with subjective evaluation scores, demonstrating effectiveness in the quantitative evaluation for COVID-19 disease progression.