Aspect-based sentiment analysis (ABSA) is an emerging fine-grained sentiment analysis task that aims to extract aspects, classify corresponding sentiment polarities and find opinions as the causes of sentiment. The latest research tends to solve the ABSA task in a unified way with end-to-end frameworks. Yet, these frameworks get fine-tuned from downstream tasks without any task-adaptive modification. Specifically, they do not use task-related knowledge well or explicitly model relations between aspect and opinion terms, hindering them from better performance. In this paper, we propose SentiPrompt to use sentiment knowledge enhanced prompts to tune the language model in the unified framework. We inject sentiment knowledge regarding aspects, opinions, and polarities into prompt and explicitly model term relations via constructing consistency and polarity judgment templates from the ground truth triplets. Experimental results demonstrate that our approach can outperform strong baselines on Triplet Extraction, Pair Extraction, and Aspect Term Extraction with Sentiment Classification by a notable margin.