The automatic extraction of relations among genes, variants, and diseases is currently an urgent problem in medical research. Previous studies on relation extraction have mainly relied on short texts from general domain corpora, and have only been able to handle binary relations within a single sentence, making it difficult to address challenges such as relation diversity, cross-sentence relations, and sparse entity distribution. To address these issues, this paper proposes a Double Graph-Based Relation Extraction method based on graph neural networks, which aims to extract gene-variant-disease ternary relations from full-text medical literature (abbreviated GVDExtractor). The proposed method effectively integrates the discourse-level information and dependency structure information of documents through the document structure graph. Then the entity relation graph provides a natural expression structure for cross-sentence relations by directly connecting edges between entities and reducing their physical distance. Results from experiments on different datasets demonstrate the effectiveness and generalization of the proposed model, providing strong support for medical research.