This paper presents a design method of a performance-adaptive controller concerned with the robust stability. A control performance in steady state is important in process control systems because the performance strongly affects qualities of products. Given this background, in order to maintain a required control performance, a performance-adaptive controller that first assesses a control performance and tunes its only a user-specified parameter based on the result has been proposed as the one-parameter tuning method. However, previous researches did not discuss about the adjustable tuning range of the parameter that can ensure the robust stability of the closed-loop system. This paper discusses about the adjustable range of the parameter that guarantees the robustness and verifies the effectiveness of the controller by simulation examples.