Document-level Event Argument Extraction (abbr., EAE) aims to extract event-related arguments from documents, including the sub-tasks of binary argument identification and role-oriented argument classification. The existing EAE approaches leverage Large Language Models (LLMs) to enhance EAE, where the capabilities of LLMs in knowledge supplementation, chain-of-thought reasoning and in-context learning enable substantial improvements to be obtained. However, current studies still suffer from insufficient demonstration examples, which provide limited guidance when LLMs predict arguments by reasoning. To address the above issue, we propose RHDG which serves as a Retrieval-augmented Heuristic-driven Demonstration Generation approach. RHDG couples retrieval-augmented generation with heuristic-driven generation, so as to generate a tailored demonstrative example from the retrieved relevant document, dynamically and felicitously. The demonstrative example is used as reference to guide the reasoning process when tackling a living EAE instance. We experiment on the benchmark dataset RAMS. The test results show that RHDG yields substantial improvements compared to the primary LLM-based EAE models like GPT-3.5, GPT-4 and LLaMA-3.1, with the performance gains of no less than 2.33%, 2.37% and 3.03% F1-scores for argument identification and 1.60%, 2.37% and 4.58% for argument classification.