In this paper we propose a new method to detumble a malfunctioning satellite. Large space debris such as malfunctioning satellites generally rotates with nutational motion. Thus several researches have proposed the methods to use a space robot for capturing and deorbiting these debris. The most of the past studies considered the method to detumble an uncontrollable satellite and then capture a single spinning satellite. However these methods require physical contact with malfunctioning satellites, which has a risk of accident. Therefore, we propose a method with an eddy current brake . The eddy current brake system can produce braking force to the target without any physical contact. Thus, we can reduce the risk of critical collision between the space robot and the target object. This paper firstly reviews dynamics of a tumbling satellite and proposes a detumbling strategy with the eddy current brake. We carry out a fundamental experiment to evaluate the performance of the braking force of the developed eddy current brake system, and then we simulate detumbling operation by using the experimental data and show an effectiveness of the proposed detumbling method.