We propose the use of neural networks to model source-side preordering for faster and better statistical machine translation. The neural network trains a logistic regression model to predict whether two sibling nodes of the source-side parse tree should be swapped in order to obtain a more monotonic parallel corpus, based on samples extracted from the word-aligned parallel corpus. For multiple language pairs and domains, we show that this yields the best reordering performance against other state-of-the-art techniques, resulting in improved translation quality and very fast decoding.