The advantages of fiber-reinforced plastic (FRP) are that it has low density and high damping capacity. However, FRP had not yet been commonly used in machine tool structures because of its low Young's modulus, cheeping characteristics, and so on. The most probable use of FRP in machine tools seems to be in combination with a conventional material like steel in order to compensate for the low Young's modulus. In this paper, the damping characteristics of a composite structure beam, which is composed of a steel pipe and FRP, were investigated both theoretically and experimentally. The effects of the fiber direction, each wall thickness of the steel pipe and the FRP on the damping capacity were clarified. It has also been made clear that if the diameter of the composite structure is permitted to increase compared with that of the original steel structure, the damping capacity can be markedly increased under the condition of constant flexural rigidity.