The stability of a prediction-based controller for LTI systems is studied in presence of time-varying input and output delays. The uncertain delay case is treated as well as the partial state knowledge case. The reduction method is used in order to prove the convergence of the closed-loop system including the state-observer, the predictor and the plant. Explicit conditions that guarantee the closed-loop stability are given thanks to a Lyapunov-Razumikhin analysis. The results are illustrated thanks to simulations.