Abstract: Neural Machine Translation (NMT) has become a popular technology in recent years, and beam search is its de facto decoding method due to the shrunk search space and reduced computational complexity. However, since it only searches for local optima at each time step through one-step forward looking, it usually cannot output the best target sentence. Inspired by the success and methodology of AlphaGo, in this paper we propose using a prediction network to improve beam search, which takes the source sentence $x$, the currently available decoding output $y_1,\cdots, y_{t-1}$ and a candidate word $w$ at step $t$ as inputs and predicts the long-term value (e.g., BLEU score) of the partial target sentence if it is completed by the NMT model. Following the practice in reinforcement learning, we call this prediction network \emph{value network}. Specifically, we propose a recurrent structure for the value network, and train its parameters from bilingual data. During the test time, when choosing a word $w$ for decoding, we consider both its conditional probability given by the NMT model and its long-term value predicted by the value network. Experiments show that such an approach can significantly improve the translation accuracy on several translation tasks.