This paper proposes a design method of a discrete time LQI control system by using a reference model. For the continuous time system, a design method of the weight matrices of the index performance for an LQI control system by using a reference model has been proposed, and this method enables us to design an LQI control system with desired transient responses easily. This method is extended to the discrete time LQI control system. But the relative order of a discrete time plant often is unity and this fact makes it difficult to transfer the continuous time method to the discrete time case directly. Therefore not only the weight matrices of the index performance but also the control system structure are designed by using a reference model. First, the design method for an SISO system is proposed, and this method is extended to an MIMO system. Numerical examples are presented to show the effectiveness of this method.