Although distributed model predictive control (MPC) has received significant attention in the literature, the robustness of distributed MPC with respect to model uncertainties and state delays has not been explicitly addressed. In this paper, a novel approach to design robust distributed MPC is proposed for polytopic uncertain systems with state delays. The algorithm requires decomposing the entire system into M subsystems and solving M linear matrix inequality optimization problems to minimize an upper bound on a robust performance objective for each subsystem. An iterative on-line algorithm for robust distributed MPC is developed to coordinate the distributed controllers. The algorithm is a flexible structure of robust control, which allows the independent computation of the state feedback laws for the subsystems. Convergence and robust stability of the proposed distributed MPC are analysed. Two numerical examples are carried out to demonstrate the effectiveness of the proposed algorithm.