Background. Chest CT findings have the potential to guide management in hospitalized patients with COVID-19. Objective. To explore a CT visual severity score in hospitalized patients with COVID-19, with attention to temporal changes in the score and the role of the score in a model for predicting in-hospital complications. Methods. This retrospective study included 161 inpatients with COVID-19 from three hospitals in China who underwent serial chest CT scans during hospitalization. CT examinations were evaluated using a visual severity scoring system. The temporal pattern of the CT visual severity score across serial CT examinations during hospitalization was characterized using a generalized spline regression model. A prognostic model to predict major complications, including in-hospital mortality, was created using the CT visual severity score and clinical variables. External model validation was performed in a cohort of 135 patients from a different hospital, evaluated by two independent radiologists. Results. The cohort included 91 survivors with non-severe disease, 55 survivors with severe disease, and 15 patients who died during hospitalization. Median CT visual lung severity score in the first week of hospitalization was 2.0 in survivors with non-severe disease, 4.0 in survivors with severe disease, and 11.0 in non-survivors. CT visual severity score peaked on hospitalization day 9 and 12 in survivors with non-severe and severe disease, respectively, and progressively decreased in subsequent hospitalization weeks in both groups. In the prognostic model, in-hospital complications were independently associated with a severe CT score (odds ratio [OR] 31.28), moderate CT score (OR 5.86), age (OR 1.09 per year increase), and lymphocyte count (OR 0.03 per 1*10^9/L increase). In the validation cohort, the two readers achieved C-index of 0.92-0.95, accuracy 85.2%-86.7%, sensitivity 70.7%-75.6%, and specificity 91.4%-91.5% for predicting in-hospital complications. Conclusion. A CT visual severity score is associated with clinical disease severity and evolves in a characteristic fashion during hospitalization for COVID-19. A prognostic model based on the CT visual severity score and clinical variables has strong performance in predicting in-hospital complications. Clinical Impact. The prognostic model using the CT visual severity score may help identify patients at highest risk of poor outcomes and guide early intervention.