A robust model predictive controller is proposed for input constrained linear systems with discrete and distributed delay in the states, where uncertainty is described by an additive bounded disturbance. The method is an extension of recently developed, tube based model predictive control to time-delay systems. A robust local controller maintains the disturbed trajectory of the controlled system in a tube whose center is the nominal trajectory and whose cross section is a robust control invariant set. Asymptotic stability of the invariant set centered on the origin is proved. Moreover, structured procedures are presented to determine offline controller parameters to guarantee closed loop stability and robustness. Online computational burden is reduced compared with the existent min-max and worst case robust predictive controllers.