This paper presents a novel user interface (UI) design framework for rehabilitation robotic system, incorporating cognitive architecture to enhance user interaction and cognitive alignment. The work focuses specifically on the design and implementation of the UI for the Wrist rehabilitation robotic system. The design framework leverages ACT-R, a cognitive architecture that models human cognitive processes through various modules including visual, motor, and goal-oriented components. A multi-stage design process is adopted, beginning with requirements analysis to determine functional needs such as state detection, training capabilities, and personalized medical services. The preliminary design stage, incorporating UI design principles and a cognitive model, is realized to create a user-centered information architecture and visual design strategy. This design is implemented in the NPU-Wrist rehabilitation robotic system, focusing on critical elements such as color contrast for visibility, icon intuitiveness for ease of use, and layout optimization based on Fitts' Law to enhance interaction efficiency. The final UI design was evaluated through the users' satisfaction questionnaire, which indicated high levels of satisfaction and validated the effectiveness of our cognitive architecture-based approach. This paper demonstrates the application of cognitive architecture in the UI design of the wrist rehabilitation robotic system, offering a methodological framework that could be adapted for broader applications in other rehabilitation robotic systems.