Uveal melanoma (UM) is the most common primary malignant intraocular tumor. The use of precision medicine for UM to enable personalized diagnosis, prognosis, and treatment require the development of computer-aided strategies and predictive tools that can identify novel high-confidence susceptibility genes (HSGs) and potential therapeutic drugs. In the present study, a computational framework via propagation modeling on integrated multi-layered molecular networks (abbreviated as iUMRG) was proposed for the systematic inference of HSGs in UM. Under the leave-one-out cross-validation experiments, the iUMRG achieved superior predictive performance and yielded a higher area under the receiver operating characteristic curve value (0.8825) for experimentally verified SGs. In addition, using the experimentally verified SGs as seeds, genome-wide screening was performed to detect candidate HSGs using the iUMRG. Multi-perspective validation analysis indicated that most of the top 50 candidate HSGs were indeed markedly associated with UM carcinogenesis, progression, and outcome. Finally, drug repositioning experiments performed on the HSGs revealed 17 potential targets and 10 potential drugs, of which six have been approved for UM treatment. In conclusion, the proposed iUMRG is an effective supplementary tool in UM precision medicine, which may assist the development of new medical therapies and discover new SGs.