This paper considers the distributed control of the LQR problem for discrete-time multi- agent systems. Distributed controllers are designed based on the solutions of centralized optimal control and the topological structure of the systems. Under mild conditions, it is shown that the distributed controller can approximate to the centralized optimal controller. Then the states of the closed-loop systems of the distributed control exponentially converge to the states of the closed-loop systems of the centralized optimal control. Some examples are given to show effectiveness of the proposed results.