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Machine learning algorithms, when applied to sensitive data, pose a potential threat to privacy. A growing body of prior work has demonstrated that membership inference attack (MIA) can disclose specific private information in the training data to an attacker. Meanwhile, the algorithmic fairness of machine learning has increasingly caught attention from both academia and industry. Algorithmic fairness ensures that the machine learning models do not discriminate a particular demographic group of individuals (e.g., black and female people). Given that MIA is indeed a learning model, it raises a serious concern if MIA ``fairly'' treats all groups of individuals equally. In other words, whether a particular group is more vulnerable against MIA than the other groups. This paper examines the algorithmic fairness issue in the context of MIA and its defenses. First, for fairness evaluation, it formalizes the notation of vulnerability disparity (VD) to quantify the difference of MIA treatment on different demographic groups. Second, it evaluates VD on four real-world datasets, and shows that VD indeed exists in these datasets. Third, it examines the impacts of differential privacy, as a defense mechanism of MIA, on VD. The results show that although DP brings significant change on VD, it cannot eliminate VD completely. Therefore, fourth, it designs a new mitigation algorithm named FAIRPICK to reduce VD. An extensive set of experimental results demonstrate that FAIRPICK can effectively reduce VD for both with and without the DP deployment.