Large Language Models (LLMs) have demonstrated their remarkable capabilities in document understanding. However, recent research reveals that LLMs still exhibit performance gaps in Document-level Relation Extraction (DocRE) as requiring fine-grained comprehension. The commonly adopted "extract entities then predict relations" paradigm in LLM-based methods leads to these gaps due to two main reasons: (1) Numerous unrelated entity pairs introduce noise and interfere with the relation prediction for truly related entity pairs. (2) Although LLMs have identified semantic associations between entities, relation labels beyond the predefined set are still treated as prediction errors. To address these challenges, we propose a novel Relation as a Prior (RelPrior) paradigm for LLM-based DocRE. For challenge (1), RelPrior utilizes binary relation as a prior to extract and determine whether two entities are correlated, thereby filtering out irrelevant entity pairs and reducing prediction noise. For challenge (2), RelPrior utilizes predefined relation as a prior to match entities for triples extraction instead of directly predicting relation. Thus, it avoids misjudgment caused by strict predefined relation labeling. Extensive experiments on two benchmarks demonstrate that RelPrior achieves state-of-the-art performance, surpassing existing LLM-based methods.