Future predictions on sequence data (e.g., videos or audios) require the algorithms to capture non-Markovian and compositional properties of high-level semantics. Context-free grammars are natural choices to capture such properties, but traditional grammar parsers (e.g., Earley parser) only take symbolic sentences as inputs. In this paper, we generalize the Earley parser to parse sequence data which is neither segmented nor labeled. This generalized Earley parser integrates a grammar parser with a classifier to find the optimal segmentation and labels, and makes top-down future predictions. Experiments show that our method significantly outperforms other approaches for future human activity prediction.