In view of the case that present demand signals of the downstream sites are not available for the upstream sites of a supply chain, a combined demand prediction scheme is proposed based on the past demand signals of downstream sites of the supply chain. Then the supply chain under consideration is modeled as an uncertain linear system with multiple state time-delays. Some delay-dependent sufficient conditions of the robust state feedback stabilization of the supply chain system and the design scheme of the controller are presented. Simulation results show that, by using the designed demand prediction method and controllers, the bullwhip effect is reduced effectively and the performance of the supply chain system is improved remarkably.