The recent surge in the field of Large Language Models (LLMs) has gained significant attention in numerous domains. In order to tailor an LLM to a specific domain such as a web-based healthcare system, fine-tuning with domain knowledge is necessary. However, two issues arise during fine-tuning LLMs for medical applications. The first is the problem of task variety, where there are numerous distinct tasks in real-world medical scenarios. This diversity often results in suboptimal fine-tuning due to data imbalance and seesawing problems. Additionally, the high cost of fine-tuning can be prohibitive, impeding the application of LLMs. The large number of parameters in LLMs results in enormous time and computational consumption during fine-tuning, which is difficult to justify. To address these two issues simultaneously, we propose a novel parameter-efficient fine-tuning framework for multi-task medical applications called MOELoRA. The framework aims to capitalize on the benefits of both MOE for multi-task learning and LoRA for parameter-efficient fine-tuning. To unify MOE and LoRA, we devise multiple experts as the trainable parameters, where each expert consists of a pair of low-rank matrices to maintain a small number of trainable parameters. Additionally, we propose a task-motivated gate function for all MOELoRA layers that can regulate the contributions of each expert and generate distinct parameters for various tasks. To validate the effectiveness and practicality of the proposed method, we conducted comprehensive experiments on a public multi-task Chinese medical dataset. The experimental results demonstrate that MOELoRA outperforms existing parameter-efficient fine-tuning methods. The implementation is available online for convenient reproduction of our experiments.