We study the problem of predicting the influence of a user in spreading fake (or real) news on social media. We propose a new model to address this problem which takes into account both user and tweet characteristics. We show that our model achieves an F1 score of 0.853, resp. 0.931, at predicting the influence of fake, resp. real, news spreaders, and outperforms existing baselines. We also investigate important features at predicting the influence of real vs. fake news spreaders.