In this paper, we consider the feedback stabilisation of an Euler-Bernoulli beam with the boundary time-delay disturbance. Due to unknown time-delay coefficient, the system might be exponentially increasing at the lack of control. We design the feedback control law based on Lyapunov function method. Different from usual use of Lyapunov function method, our approach is to combine the construction of Lyapunov functionals with the controller design, which will guarantee the system energy function decays exponentially. In this procedure, we deduce the inequality equations satisfied by the system parameters. We prove the well-posedness of the corresponding closed-loop system by using semigroup theory and the inequality equations are solvable. Moreover, the exponential decay rate of the system is estimated. In addition, some numerical simulations are also presented to support the obtained results.