Solar sail is a novel spacecraft and has the potential applications in the near future. The large amplitude vibration should be considered because it is characterized by its huge and lightweight structure. In this paper, the supporting beam of solar sail is regarded as the most important structure and used to model the sailcraft as it accounts for most of the mechanical energies when it is in deformed configuration, also as the Euler beam can model the bending motion dominant sailcraft when it experiences attitude motions. The structural dynamics of solar sail supporting beam with geometric nonlinearity undergoing the forces generated by solar radiation pressure, sliding masses and control vanes are presented. The axial and transverse vibration equations with the properties of strong coupling, nonlinearity and time-varying coefficient matrices are obtained by using Lagrange equation method after calculating the related energies and works. The vibration equations are transformed into nonlinear algebraic equations utilizing implicit unconditionally stable Newmark-β algorithm for each time step. The nonlinear algebraic equations are solved by Newton-iterative algorithm. We compute and analyze the linear and nonlinear vibration responses affected by the mass and velocity of the sliding mass, the angular velocity of the force generated by control vane in detail. The computational results indicate that the mass and velocity of sliding mass affect the vibration responses (including the vibration frequency), but the angular velocity of the force generated by control vane hardly affects the vibration responses. Moreover, the linear and nonlinear vibrations are distinct obviously by comparing the linear and nonlinear responses. It is demonstrated that the geometric nonlinearity of the highly-flexible structure should be considered for performing vibration analysis exactly, and the vibration responses excited by the prescribed motion of the attitude control actuators should be analyzed carefully.