In this paper, we study the eventual periodicity of the following fuzzy max-type difference equationwhere {α n } n 0 is a periodic sequence of positive fuzzy numbers and the initial values z −d , z −d+1 , . . . , z −1 are positive fuzzy numbers with d = max{m, r}. We show that if max(supp α n ) < 1, then every positive solution of this equation is eventually periodic with period 2m.