We present a new model for probabilistic forecasting using graph-based rating method. We provide a \forward-looking" type graph-based approach and apply it to predict football game outcomes by simply using the historical game results data of the investigated competition. The assumption of our model is that the rating of the teams after a game day correctly reflects the actual relative performance of them. We consider that the smaller the changing of the rating vector {contains the ratings of each team { after a certain outcome in an upcoming single game, the higher the probability of that outcome. Performing experiments on European foot- ball championships data, we can observe that the model performs well in general and outperforms some of the advanced versions of the widely-used Bradley-Terry model in many cases in terms of predictive accuracy. Although the application we present here is special, we note that our method can be applied to forecast general graph processes.