In Natural Language Processing(NLP), Event Temporal Relation Extraction (ETRE) is to recognize the temporal relations of two events. Prior studies have noted the importance of language models for ETRE. However, the restricted pre-trained knowledge of Small Language Models(SLMs) limits their capability to handle minority class relations in imbalanced classification datasets. For Large Language Models(LLMs), researchers adopt manually designed prompts or instructions, which may introduce extra noise, leading to interference with the model's judgment of the long-distance dependencies between events. To address these issues, we propose GDLLM, a Global Distance-aware modeling approach based on LLMs. We first present a distance-aware graph structure utilizing Graph Attention Network(GAT) to assist the LLMs in capturing long-distance dependency features. Additionally, we design a temporal feature learning paradigm based on soft inference to augment the identification of relations with a short-distance proximity band, which supplements the probabilistic information generated by LLMs into the multi-head attention mechanism. Since the global feature can be captured effectively, our framework substantially enhances the performance of minority relation classes and improves the overall learning ability. Experiments on two publicly available datasets, TB-Dense and MATRES, demonstrate that our approach achieves state-of-the-art (SOTA) performance.