This paper investigates the self-bias in large language models (LLMs) during self-refinement. We define self-bias as the tendency of LLMs to favor their own generated outputs. Using two statistical measures—bias and distance skewness—we analyze six LLMs (GPT-4, GPT-3.5, Gemini, LLaMA2, Mixtral, and DeepSeek) across three tasks: machine translation, constrained text generation, and mathematical reasoning. Our findings show that self-bias is prevalent in all examined LLMs across multiple languages and tasks. While the self-refine pipeline improves fluency and understandability, it also amplifies self-bias. To mitigate this bias, we find that larger model sizes and external feedback with accurate assessment significantly reduce bias, leading to performance improvements in downstream tasks. The study highlights that self-bias can lead to false positive corrections and reduced diversity in text generation. We propose two solutions to address self-bias: increasing model size and incorporating external feedback. Our results show that external feedback can significantly reduce self-bias, and larger models are more resistant to self-bias. The study contributes to the understanding of self-bias in LLMs and provides insights into improving their performance through self-refinement.This paper investigates the self-bias in large language models (LLMs) during self-refinement. We define self-bias as the tendency of LLMs to favor their own generated outputs. Using two statistical measures—bias and distance skewness—we analyze six LLMs (GPT-4, GPT-3.5, Gemini, LLaMA2, Mixtral, and DeepSeek) across three tasks: machine translation, constrained text generation, and mathematical reasoning. Our findings show that self-bias is prevalent in all examined LLMs across multiple languages and tasks. While the self-refine pipeline improves fluency and understandability, it also amplifies self-bias. To mitigate this bias, we find that larger model sizes and external feedback with accurate assessment significantly reduce bias, leading to performance improvements in downstream tasks. The study highlights that self-bias can lead to false positive corrections and reduced diversity in text generation. We propose two solutions to address self-bias: increasing model size and incorporating external feedback. Our results show that external feedback can significantly reduce self-bias, and larger models are more resistant to self-bias. The study contributes to the understanding of self-bias in LLMs and provides insights into improving their performance through self-refinement.