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In this paper, we study the group decision making problem with linguistic preference relations. We first show that the weighted combination of A₁,A₂,…,A_m is linguistic preference relation under the condition that all of A₁,A₂,…,A_m are linguistic preference relations. Then we define the concepts of deviation degree and similarity degree between two linguistic values, and deviation degree and similarity degree between two linguistic preference relations. We also show that the deviation degree between linguistic preference relation A_i of A₁,A₂,…,A_m and their group linguistic preference relation is no greater than the largest deviation degree between the linguistic preference relation A_i and each of the linguistic preference relations A₁,A₂,…,A_m. Thus, a theoretic basis has been established for the application of linguistic preference relations in group decision making.