As they have a vital effect on social decision-making, AI algorithms not only should be accurate and but also should not pose unfairness against certain sensitive groups (e.g., non-white, women). Various specially designed AI algorithms to ensure trained AI models to be fair between sensitive groups have been developed. In this paper, we raise a new issue that between-group fair AI models could treat individuals in a same sensitive group unfairly. We introduce a new concept of fairness so-called within-group fairness which requires that AI models should be fair for those in a same sensitive group as well as those in different sensitive groups. We materialize the concept of within-group fairness by proposing corresponding mathematical definitions and developing learning algorithms to control within-group fairness and between-group fairness simultaneously. Numerical studies show that the proposed learning algorithms improve within-group fairness without sacrificing accuracy as well as between-group fairness.