In this paper, the modeling and vibration control problem of a satellite with two flexible solar panels are addressed. Symmetric flexible solar panels attached to the center body are used to represent the dynamics of flexible satellite system. The left and the right panels are modeled as two Euler-Bernoulli beams and the main body of the satellite is modeled as a lumped mass in the center of two panels. The single-point control input is applied at the center body to suppress the vibrations of both panels. Based on the construction of a physically motivated Lyapunov function, the exponential stability is proved with the proposed control. Both the control design and the stability analysis are based on the original infinite-dimensional dynamic equations. Numerical examples illustrate the effectiveness of the proposed control system.