In this paper, we consider a design of the model reference control systems with adjustable parameters for linear systems with time-varying parametric uncertainties. To discuss this problem, we focus on the output error between the plant and the reference model, and adopt the reachable domain of this error as a performance index. This reachable domain is known as an output reachable set. Based on the analysis technique of output reachable sets, we propose a new design technique of the model reference controller, and demonstrate its efficacy by numerical case studies.