In this paper, we study the problem of memory dynamic output feedback (MDOF) controller design for discrete-time systems subject to finite frequency disturbances, i.e., the low, middle, or high frequency range. In order to reduce controller design conservatism, a kind of memory control strategy is developed, which fully utilizes the useful past controller states. Our objective is to design a MDOF controller such that the closed-loop system is asymptotically stable with prescribed finite frequency H∞ performance. Based on the generalized Kalman-Yakubovich-Popov (GKYP) lemma, sufficient conditions are derived for the design of satisfactory MDOF controllers. The controller gains together with the optimal finite frequency H∞ performance can be obtained by solving a convex optimization algorithm in terms of linear matrix inequalities (LMIs). Finally, simulation studies are given the show the effectiveness of the proposed control approach.