Action prediction on a partially observed action sequence is a very challenging task. To address this challenge, we first design a global-local distance model, where a global-temporal distance compares subsequences as a whole and local-temporal distance focuses on individual segment. Our distance model introduces temporal saliency for each segment to adapt its contribution. Finally, a global-local temporal action prediction model is formulated in order to jointly learn and fuse these two types of distances. Such a prediction model is capable of recognizing action of: 1) an on-going sequence and 2) a sequence with arbitrarily frames missing between the beginning and end (known as gap-filling). Our proposed model is tested and compared with related action prediction models on BIT, UCF11, and HMDB data sets. The results demonstrated the effectiveness of our proposal. In particular, we showed the benefit of our proposed model on predicting unseen action types and the advantage on addressing the gapfilling problem as compared with recently developed action prediction models.