In this paper we describe the application of an H-infinity system identification procedure to a Tokamak. The work is motivated by the need to create linear models which are suitable for controller design and which may be used to validate different models derived from physics principles. The paper develops an H-infinity system identification algorithm and demonstrates its successful application to the Tokamak a configuration variable (TCV). Each of the required steps is detailed, from the design of identification experiments through to the creation of low-order models from a combination of Hankel model reduction and Chebycheff approximation. The method described in this paper is a worst-case identification technique, in that it aims to minimize the H-infinity error between the identified model and the true plant. Such a model is particularly well suited for robust controller design. The identified model of TCV is compared with various physics-based models.