Lexicography minimum solution is defined to describe a system of fuzzy relation inequality(FRI) with max-min composition is introduced in this paper. It can be applied to P2P file sharing system when we consider its priority rank of the terminals of the networking. The concepts and properties of lexicography relation and lexicography minimum solution are studied, and an algorithm for lexicography minimum solution is proposed by constructing n programming problems, which is effective and flexible and illustrated by an application example.