This article presents a distributed model predictive controller (MPC) based on linear models that use input/output plant data and D-ADMM optimization. The use of input/output models has the advantage of not requiring a Kalman filter to estimate the plant state. The D-ADMM algorithm solves the optimization problem associated to a cost function that is the sum of the control agents private costs, being a modification of the Alternating Direction of Multipliers (ADMM) algorithm that requires no central node and implies a significant reduction in the communication among adjacent nodes. The distributed MPC is obtained for the special case of a linear graph. An application to distributed control of a water delivery canal is presented to illustrate the algorithm.