Despite the rapid development and great success of machine learning models, extensive studies have exposed their disadvantage of inheriting latent discrimination and societal bias from the training data. This phenomenon hinders their adoption on high-stake applications. Thus, many efforts have been taken for developing fair machine learning models. Most of them require that sensitive attributes are available during training to learn fair models. However, in many real-world applications, it is usually infeasible to obtain the sensitive attributes due to privacy or legal issues, which challenges existing fair-ensuring strategies. Though the sensitive attribute of each data sample is unknown, we observe that there are usually some non-sensitive features in the training data that are highly correlated with sensitive attributes, which can be used to alleviate the bias. Therefore, in this paper, we study a novel problem of exploring features that are highly correlated with sensitive attributes for learning fair and accurate classifiers. We theoretically show that by minimizing the correlation between these related features and model prediction, we can learn a fair classifier. Based on this motivation, we propose a novel framework which simultaneously uses these related features for accurate prediction and enforces fairness. In addition, the model can dynamically adjust the regularization weight of each related feature to balance its contribution on model classification and fairness. Experimental results on real-world datasets demonstrate the effectiveness of the proposed model for learning fair models with high classification accuracy.