Syntactic and pragmatic completeness is known to be important for turn-taking prediction, but so far machine learning models of turn-taking have used such linguistic information in a limited way. In this paper, we introduce TurnGPT, a transformer-based language model for predicting turn-shifts in spoken dialog. The model has been trained and evaluated on a variety of written and spoken dialog datasets. We show that the model outperforms two baselines used in prior work. We also report on an ablation study, as well as attention and gradient analyses, which show that the model is able to utilize the dialog context and pragmatic completeness for turn-taking prediction. Finally, we explore the model’s potential in not only detecting, but also projecting, turn-completions.