Sentiment forecasting in dialog aims to predict the polarity of next utterance to come, and can help speakers revise their utterances in sentimental utterances generation. However, the polarity of next utterance is normally hard to predict, due to the lack of content of next utterance (yet to come). In this study, we propose a Neural Sentiment Forecasting (NSF) model to address inherent challenges. In particular, we employ a neural simulation model to simulate the next utterance based on the context (previous utterances encountered). Moreover, we employ a sequence influence model to learn both pair-wise and seq-wise influence. Empirical studies illustrate the importance of proposed sentiment forecasting task, and justify the effectiveness of our NSF model over several strong baselines.