Abstract: Based on Timoshenko beam theory and a Hamiltonian principle, the governing equation of transverse vibration of a free-free axially moving beam under an axial compressive load is established. The vibration characteristics of the beam are obtained by the analytical solution and Differential Quadrature Method (DQM). The effect of compressive load and axially moving speed along with a load derivative and an axial acceleration on natural frequencies is studied. The analyzing results show that the compressive load and the axially moving cause the natural frequency decreased. A supercritical phenomenon appears while the compressive load is high and the beam undergoes a coupled-mode flutter. The instability of the beam fundamental frequency happens under load derivative and acceleration effects; the critical load decreases as the moving speed increases, and the critical speed reduces with the increase of a compressive load.