This paper is concerned with robust model predictive control for linear continuous uncertain systems with state delay and control constraints.A piecewise constant control sequence is calculated by minimizing the upper-bound of the infinite horizon quadratic cost function.At each sampling time,the sufficient conditions for the existence of the model predictive control are derived.and expressed as a set of linear matrix inequalities.The robust stability of the closed-loop systems is guaranteed by the proposed design method.A numerical example is given to illustrate the main results.