Objective: To optimize in-context learning in biomedical natural language processing by improving example selection. Methods: We introduce a novel multi-mode retrieval-augmented generation (MMRAG) framework, which integrates four retrieval strategies: (1) Random Mode, selecting examples arbitrarily; (2) Top Mode, retrieving the most relevant examples based on similarity; (3) Diversity Mode, ensuring variation in selected examples; and (4) Class Mode, selecting category-representative examples. This study evaluates MMRAG on three core biomedical NLP tasks: Named Entity Recognition (NER), Relation Extraction (RE), and Text Classification (TC). The datasets used include BC2GM for gene and protein mention recognition (NER), DDI for drug-drug interaction extraction (RE), GIT for general biomedical information extraction (RE), and HealthAdvice for health-related text classification (TC). The framework is tested with two large language models (Llama2-7B, Llama3-8B) and three retrievers (Contriever, MedCPT, BGE-Large) to assess performance across different retrieval strategies. Results: The results from the Random mode indicate that providing more examples in the prompt improves the model's generation performance. Meanwhile, Top mode and Diversity mode significantly outperform Random mode on the RE (DDI) task, achieving an F1 score of 0.9669, a 26.4% improvement. Among the three retrievers tested, Contriever outperformed the other two in a greater number of experiments. Additionally, Llama 2 and Llama 3 demonstrated varying capabilities across different tasks, with Llama 3 showing a clear advantage in handling NER tasks. Conclusion: MMRAG effectively enhances biomedical in-context learning by refining example selection, mitigating data scarcity issues, and demonstrating superior adaptability for NLP-driven healthcare applications.