Abstract The aspect-based sentiment triplet extraction (ASTE), as a complete sentiment analysis task, aims to recognize the aspect term, the opinion expression, and the sentiment polarity in a sentence. Current state-of-the-art ASTE models employ a joint extracting scheme for better task improvements. However, how to better solve the triplet overlap issues in the task, and effectively model the mutual interactions between the triplet structures remain challenging. In this work, we explore a neural transition model for end-to-end ASTE. We model the triplet prediction as a graph structure, based on which we implement a transition system with neural design. We further propose a triplet memory mechanism to fully leverage the underlying interactions from the previously recognized triplets relevant to the current parse. We experiment on the benchmark datasets, and the results show that our model achieved state-of-the-art performances against current baselines, meanwhile being more efficient on decoding. Further analysis is conducted to verify the effectiveness of our transition framework.