In this paper, we investigate the exponential stability of a Timoshenko beam with interior time delays and boundary damping. At first, we show that the system is well posed by the semigroup method. Next, we construct an appropriate functional to study the exponential stability. We transform the exponential stability into the solvability of inequality equations, and then by analysing the relationship between delays parameters alpha(1), alpha(2) and damping parameters beta(1), beta(2), we describe the (alpha(1), alpha(2))-region for which the system is exponentially stable.