Aspect-based Sentiment Analysis (ABSA) is a sentiment analysis task at fine-grained level. Recently, generative frameworks have attracted increasing attention in ABSA due to their ability to unify subtasks and their continuity to upstream pre-training tasks. However, these generative models suffer from the neighboring dependency problem that induces neighboring words to get higher attention. In this paper, we propose SynGen, a plug-and-play syntactic information aware module. As a plug-in module, our SynGen can be easily applied to any generative framework backbones. The key insight of our module is to add syntactic inductive bias to attention assignment and thus direct attention to the correct target words. To the best of our knowledge, we are the first one to introduce syntactic information to generative ABSA frameworks. Our module design is based on two main principles: (1) maintaining the structural integrity of backbone PLMs and (2) disentangling the added syntactic information and original semantic information. Empirical results on four popular ABSA datasets demonstrate that SynGen enhanced model achieves a comparable performance to the state-of-the-art model with relaxed labeling specification and less training consumption.