Combining different therapies synergistically is an essential aspect of developing effective treatments. Although there is a wealth of research on computational prediction for new combination therapies, there is limited to no research on combination therapies in the treatment of viral diseases. This paper proposes AI-based models for predicting novel antiviral combinations to treat virus diseases synergistically. To do this, we assembled a comprehensive dataset comprising information on viral strains, drug compounds, and their known interactions. As far as we know, this is the first dataset and learning model on combination therapy for viruses. Our proposal includes a deep model and two machine learning models to optimize combination therapy. The machine learning models showed the highest performance among all methods, and the predicted values were validated by t-test, indicating the effectiveness of the proposed methods. One of the predicted combinations of acyclovir and ribavirin has been experimentally confirmed to have a synergistic antiviral effect against herpes simplex type-1 virus, as described in the literature.