This paper investigated the optimal vibration control of flexible beams subjected to a moving mass with constant speed. We established the vibration equation of time-variant systems of a moving mass-flexible beam based on the vibration theory of the flexible beam. The model considered the coupling effect between the moving mass and the vibration of the flexible beam. We determined the terminal time instant when the moving mass left the beam and established the free vibration equation of time-invariant systems. Some methods suitable for time-invariant systems would lead to a suboptimal effect when applied to time-variant systems. Consequently, the above problems were analyzed using several control methods. The paper then discussed optimal control results of different actuation solutions. The numerical results indicated that the use of time-varying control strategy was more effective when actuator locations were determined. The optimal results with respect to the performance index were obtained by the state-dependent Riccati equation. For the time-varying system, bang-bang control performed more poorly compared with the bound linear quadratic regulator control in an augmented form, which was optimal corresponding to the performance index.