Generating synthetic datasets via large language models (LLMs) themselves has emerged as a promising approach to improve LLM performance. However, LLMs inherently reflect biases present in their training data, leading to a critical challenge: when these models generate synthetic data for training, they may propagate and amplify their inherent biases that can significantly impact model fairness and robustness on downstream tasks--a phenomenon we term bias inheritance. This work presents the first systematic investigation in understanding, analyzing, and mitigating bias inheritance. We study this problem by fine-tuning LLMs with a combined dataset consisting of original and LLM-augmented data, where bias ratio represents the proportion of augmented data. Through systematic experiments across 10 classification and generation tasks, we analyze how 6 different types of biases manifest at varying bias ratios. Our results reveal that bias inheritance has nuanced effects on downstream tasks, influencing both classification tasks and generation tasks differently. Then, our analysis identifies three key misalignment factors: misalignment of values, group data, and data distributions. Based on these insights, we propose three mitigation strategies: token-based, mask-based, and loss-based approaches. Experiments demonstrate that these strategies also work differently on various tasks and bias, indicating the substantial challenges to fully mitigate bias inheritance. We hope this work can provide valuable insights to the research of LLM data augmentation.