Missing values are ubiquitous in real-world datasets and are known to cause unfairness in a machine learning algorithm's decision-making process. However, there has been limited work that aims to mitigate the unfairness associated with missing data imputation. In this paper, we first derive a positive information-theoretic lower bound for the imputation fairness when using ground-truth conditional distribution for missing data imputation. Furthermore, we propose a novel missing data imputation model, known as fairness-aware imputation GAN (FIGAN), which provides accurate imputations while achieving imputation fairness. Through experiments, we illustrate that FIGAN can significantly improve imputation fairness, compared to the existing imputation methods. At the same time, FIGAN can also achieve competitive imputation accuracy.