In spite of the potential for ground-breaking achievements offered by large language models (LLMs) (e.g., GPT-3), they still lag significantly behind fully-supervised baselines (e.g., fine-tuned BERT) in relation extraction (RE). This is due to the two major shortcomings of LLMs in RE: (1) low relevance regarding entity and relation in retrieved demonstrations for in-context learning; and (2) the strong inclination to wrongly classify NULL examples into other pre-defined labels. In this paper, we propose GPT-RE to bridge the gap between LLMs and fully-supervised baselines. GPT-RE successfully addresses the aforementioned issues by (1) incorporating task-specific entity representations in demonstration retrieval; and (2) enriching the demonstrations with gold label-induced reasoning logic. We evaluate GPT-RE on four widely-used RE datasets, and observe that GPT-RE achieves improvements over not only existing GPT-3 baselines, but also fully-supervised baselines. Specifically, GPT-RE achieves SOTA performances on the Semeval and SciERC datasets, and competitive performances on the TACRED and ACE05 datasets.