This paper presents a fixed-order H-infinity controller design based on linear matrix inequalities for multi-input-multi-output systems. The main difficulty in the development of a fixed-order controller design is that the associated solution set of the problem is defined in a non-convex cluster, and that makes the problem computationally intractable. The convex inner approximation is used to deal with this non-convexity. The proposed controller design approach is applied to some elegant numerical problems taken from various previous works. To show the effectiveness of the proposed method, the full-order H-infinity controller and fixed-order controllers are constructed for these models using the traditional method and popular toolboxes, respectively. Furthermore, in this paper, some strategies for choosing the central polynomial, which is the main conservatism of the proposed method, are discussed.