Background: Medical disputes are common in hospitals and a major challenge for the operations of medical institutions. However, few studies have looked into the association between medical disputes and hospital legal constructions. The purpose of the study was to investigate the relationship between hospital legal constructions and medical disputes, and it also aimed to develop a nomogram to estimate the likelihood of medical disputes. Methods: Between July and September 2021, 2,716 administrators from 130 hospitals were enrolled for analysis. The study collected seventeen variables for examination. To establish a nomogram, administrators were randomly split into a training group (n = 1,358) and a validation group (n = 1,358) with a 50:50 ratio. The nomogram was developed using data from participants in the training group, and it was validated in the validation group. The nomogram contained significant variables that were linked to medical disputes and were identified by multivariate analysis. The nomogram's predictive performance was assessed utilizing discriminative and calibrating ability. A web calculator was developed to be conducive to model utility. Results: Medical disputes were observed in 41.53% (1,128/2,716) of participants. Five characteristics, including male gender, higher professional ranks, longer length of service, worse understanding of the hospital charters, and worse construction status of hospital rule of law, were significantly associated with more medical disputes based on the multivariate analysis. As a result, these variables were included in the nomogram development. The AUROC was 0.67 [95% confident interval (CI): 0.64-0.70] in the training group and 0.68 (95% CI: 0.66-0.71) in the validation group. The corresponding calibration slopes were 1.00 and 1.05, respectively, and intercepts were 0.00 and -0.06, respectively. Three risk groups were created among the participants: Those in the high-risk group experienced medical disputes 2.83 times more frequently than those in the low-risk group (P < 0.001). Conclusion: Medical dispute is prevailing among hospital administrators, and it can be reduced by the effective constructions of hospital rule of law. This study proposes a novel nomogram to estimate the likelihood of medical disputes specifically among administrators in tertiary hospitals, and a web calculator can be available at https://ymgarden.shinyapps.io/Predictionofmedicaldisputes/.