Generating synthetic datasets via large language models (LLMs) has emerged as a promising approach to improve LLM performance. However, LLMs inherently reflect biases in their training data, leading to a critical challenge: when models are trained on synthetic data, they may propagate and amplify the inherent biases that can significantly impact 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 fine-tune LLMs with a combined dataset of real and LLM-augmented data with varied bias ratio as the proportion of augmented data. Through systematic experiments across 10 classification and generation tasks, we analyze how 6 different types of biases manifest. Our results indicate that bias inheritance harms downstream task performance in bias directly-related classification and generation tasks. 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, which can work differently on various tasks and bias, indicating the substantial challenges to mitigate bias inheritance. We hope this work can provide insights to the research of LLM data augmentation.