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While artificial intelligence (AI)-based decision-making systems are increasingly popular, significant concerns on the potential discrimination during the AI decision-making process have been observed. For example, the distribution of predictions is usually biased and dependents on the sensitive attributes (e.g., gender and ethnicity). Numerous approaches have therefore been proposed to develop decision-making systems that are discrimination-conscious by-design, which are typically batch-based and require the simultaneous availability of all the training data for model learning. However, in the real-world, the data streams usually come on the fly which requires the model to process each input data once ``on arrival'' and without the need for storage and reprocessing. In addition, the data streams might also evolve over time, which further requires the model to be able to simultaneously adapt to non-stationary data distributions and time-evolving bias patterns, with an effective and robust trade-off between accuracy and fairness. In this paper, we propose a novel framework of online decision tree with fairness in the data stream with possible distribution drifting. Specifically, first, we propose two novel fairness splitting criteria that encode the data as well as possible, while simultaneously removing dependence on the sensitive attributes, and further adapts to non-stationary distribution with fine-grained control when needed. Second, we propose two fairness decision tree online growth algorithms that fulfills different online fair decision-making requirements. Our experiments show that our algorithms are able to deal with discrimination in massive and non-stationary streaming environments, with a better trade-off between fairness and predictive performance.