Machine learning algorithms are commonly being deployed in decision-making systems that have a direct impact on human lives. However, if these algorithms are trained solely to minimize training/test errors, they may inadvertently discriminate against individuals based on their sensitive attributes, such as gender, race or age. Recently, algorithms that ensure the fairness are developed in the machine learning community. Fairness criteria are applied by these algorithms to measure the fairness, but they often use the point estimate to assess the fairness and fail to consider the uncertainty of the sample fairness criterion once the algorithms are deployed. We suggest that assessing the fairness should take the uncertainty into account. In this paper, we use the covariance as a proxy for the fairness and develop the confidence region of the covariance vector using empirical likelihood \citep{Owen1988}. Our confidence region based fairness constraints for classification take uncertainty into consideration during fairness assessment. The proposed confidence region can be used to test the fairness and impose fairness constraint using the significant level as a tool to balance the accuracy and fairness. Simulation studies show that our method exactly covers the target Type I error rate and effectively balances the trade-off between accuracy and fairness. Finally, we conduct data analysis to demonstrate the effectiveness of our method.