This article is concerned with the local stabilization problem for discrete-time systems with both distributed state delay and fast-varying input delay under actuator saturations. By introducing some terms concerning the distributedly delayed state and the current state, a novel polytopic model is first proposed to characterize the delayed saturation nonlinearity. Then, by incorporating a piecewise Lyapunov functional and some summation inequalities, a sufficient condition is established by means of linear matrix inequalities under which the closed-loop system is locally exponentially stable. Moreover, the conditions for two special cases with single state delay and single input delay are proposed. Subsequently, certain optimization problems are formulated with aim to maximize the estimate of the region of attraction. Finally, two examples show the effectiveness and values of the obtained results.