Esophageal varices (EV), a serious health concern resulting from portal hypertension, are traditionally diagnosed through invasive endoscopic procedures. Despite non-contrast computed tomography (NC-CT) imaging being a less expensive and non-invasive imaging modality, it has yet to gain full acceptance as a primary clinical diagnostic tool for EV evaluation. To overcome existing diagnostic challenges, we present the Multi-Organ-cOhesion-Network (MOON), a novel framework enhancing the analysis of critical organ features in NC-CT scans for effective assessment of EV. Drawing inspiration from the thorough assessment practices of radiologists, MOON establishes a cohesive multiorgan analysis model that unifies the imaging features of the related organs of EV, namely esophagus, liver, and spleen. This integration significantly increases the diagnostic accuracy for EV. We have compiled an extensive NC-CT dataset of 1,255 patients diagnosed with EV, spanning three grades of severity. Each case is corroborated by endoscopic diagnostic results. The efficacy of MOON has been substantiated through a validation process involving multi-fold cross-validation on 1,010 cases and an independent test on 245 cases, exhibiting superior diagnostic performance compared to methods focusing solely on the esophagus (for classifying severe grade: AUC of 0.864 versus 0.803, and for moderate to severe grades: AUC of 0.832 versus 0.793). To our knowledge, MOON is the first work to incorporate a synchronized multi-organ NC-CT analysis for EV assessment, providing a more acceptable and minimally invasive alternative for patients compared to traditional endoscopy.