Fair clustering aims to hide sensitive attributes during data partition by balancing the distribution of protected subgroups in each cluster. Existing work attempts to address this problem by reducing it to a classical balanced clustering with a constraint on the proportion of protected subgroups of the input space. However, the input space may limit the clustering performance, and so far only low-dimensional datasets have been considered. In light of these limitations, in this paper, we propose Deep Fair Clustering (DFC) to learn fair and clustering-favorable representations for clustering simultaneously. Our approach could effectively filter out sensitive attributes from representations, and also lead to representations that are amenable for the following cluster analysis. Theoretically, we show that our fairness constraint in DFC will not incur much loss in terms of several clustering metrics. Empirically, we provide extensive experimental demonstrations on four visual datasets to corroborate the superior performance of the proposed approach over existing fair clustering and deep clustering methods on both cluster validity and fairness criterion.