This paper studies the stability problem for norm-bounded uncertain discrete system with both state and input multiple delays. According to Lyapunov method ,by using technique of linear matrix inequalities (LMI) and bilinear matrix inequalities (BMI)，this article addresses a novel sufficient condition for the stability of the system and designs a state feedback robust controller which is numerically feasible with Matlab LMI control Toolbox for the closed loop system. An effective alternate iterative algorithm for the guaranteed cost is proposed via convex optimal techniques. In the end, a simulation case is provided to illustrate the correctness and the effectiveness of the proposed theoretical result and algorithm.