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The hesitant fuzzy set (HFS) can reflect the hesitation and uncertainty of decision-makers for the reason that it uses some possible values instead of a certain value. Considering that there is still no research on concept lattice or fuzzy formal concept analysis (FFCA) in a hesitant fuzzy environment, in this paper, we propose the definition and the related theory of hesitant fuzzy concept lattice. Firstly, we propose the hesitant fuzzy formal concept analysis theory and study the definition of hesitant fuzzy concept lattice. Secondly, we provide two effective reduction methods of hesitant fuzzy formal context and discuss the differences of them. Thirdly, we propose an incremental construction algorithm to construct the hesitant fuzzy concept lattice. After that, we study the similarity calculation method of hesitant fuzzy concepts. Finally, we design a practical application to validate the hesitant fuzzy concept lattice theory, which is proven to be correct and effective.