Large language models (LLMs) are increasingly used as evaluators in natural language generation tasks, offering advantages in scalability and interpretability over traditional evaluation methods. However, existing LLM-based evaluations often suffer from biases and misalignment, particularly in domain-specific tasks, due to limited functional understanding and knowledge gaps. To address these challenges, we first investigate the relationship between an LLM-based evaluator’s familiarity with the target task and its evaluation performance. We then introduce the Co-Eval framework, which leverages a criteria planner model and optimized machine metrics to enhance the scalability and fairness of LLM-based evaluation. Experimental results on both general and domain-specific tasks demonstrate that Co-Eval reduces biases, achieving up to a 0.4903 reduction in self-preference bias, and improves alignment with human preferences, with gains of up to 0.324 in Spearman correlation.