Abstract: Based on Euler beam theory, the transverse vibration of an axially moving, initially tensioned beam made of functionally graded materials is investigated. The material properties are assumed to vary continuously through the thickness of the beam according to a power law distribution. The Hamilton’s principle is employed to derive the governing equation and the complex mode approach is performed to obtain the transverse vibration modes and natural frequencies, respectively. The effects of some parameters including axially moving speed, the power-law exponent and the initial stress on the dynamic responses are examined and revealed in detail. The results show that an increase in the power-law exponent or the axial speed results in a lower natural frequency, while the axial initial stress tends to increase the natural frequency.