Large Language Models (LLMs) have demonstrated impressive performance across diverse domains, yet they still encounter challenges such as insufficient domain-specific knowledge, biases, and hallucinations. This underscores the need for robust evaluation methodologies to accurately assess LLM-based applications. Traditional evaluation methods, which rely on word overlap or text embeddings, are inadequate for capturing the nuanced semantic information necessary to evaluate dynamic, open-ended text generation. Recent research has explored leveraging LLMs to mimic human reasoning and decision-making processes for evaluation purposes known as LLM-as-a-judge framework. However, these existing frameworks have two significant limitations. First, they lack the flexibility to adapt to different text styles, including various answer and ground truth styles, thereby reducing their generalization performance. Second, the evaluation scores produced by these frameworks are often skewed and hard to interpret, showing a low correlation with human judgment. To address these challenges, we propose a novel dynamic multi-agent system that automatically designs personalized LLM judges for various natural language generation applications. This system iteratively refines evaluation prompts and balances the trade-off between the adaptive requirements of downstream tasks and the alignment with human perception. Our experimental results show that the proposed multi-agent LLM Judge framework not only enhances evaluation accuracy compared to existing methods but also produces evaluation scores that better align with human perception.