Formal concept analysis is an important mathematical tool for knowledge representation and knowledge discovery. Attribute reduction is a crucial research issue attracting many attention of researchers on formal concept analysis. This paper proposes one type of attribute reduction of formal context, in which all join-irreducible elements of a concept lattice are preserved. The join-irreducible elements of a formal context and their properties are first discussed. Then, the concept of join-irreducible-attribute reduction of formal context is then introduced. Finally, an equivalence condition of join-irreducible-consistent attribute set is given.