In the present paper we consider the boundary feedback stabilization of a Timoshenko beam with both ends free. We propose boundary feedback control law that makes the closed loop system dissipative. Using asymptotic analysis techniques, we give explicit asymptotic formula of eigenvalues of the closed loop system, and prove the Riesz basis property of eigenvectors and generalized eigenvectors. By a detailed analysis of spectrum of the closed loop system, we show that the closed system is exponentially stable.