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This paper presents stability analysis for an impedance control of a specific robot system in a human-robot cooperative task system. In the stability analysis, we consider these conditions such as an impedance characteristic of the robot, time delay of a human operator and a control of the robot, a compliance of structure of the robot, and an environment stiffness respectively. The stability analysis simulation reveals that these conditions have significant influence on the stability of the system. In order to investigate the usefulness of the stability analysis simulation, a verification experiment using a Mitsubishi PA-10 robot arm was carried out. Experimental results illustrate that the investigated stability analysis is useful and effective to simulate and reveal the stability of the human-robot cooperative task system.