The axially moving beam is a simplified model for many aircraft structures. The elasticity is patently obvious with slenderness increased and quality reduced, and the velocity has significant effect on vibration characteristics at the same time. The dynamic equation of transverse vibration of axially moving beam, subjected to a transverse excitation is derived from Hamilton’s principle. At first, dimensionless method and complex modal analysis method are applied to simplify the equation as there is an axial force or not respectively, also the frequency equation and modal function can be determined, which can be calculated using numerical method. Then, the decoupling method is used to simplify the control equation into a set of differential equations, the displacement response of transverse vibration is yielded after solving that equations. Finally, random response’s correlation function is calculated by using the method of mathematical statistics, and the random response spectrum is given via Fourier transform. The numerical example illustrates that velocity could affect vibration characteristics and random response significantly.