In this paper,robust asymptotic stability for uncertain discrete systems with interval time-varying delay and nonlinear perturbations is considered.Novel Lyapunov functionals and delay-partitioning approach are proposed are proposed to guarantee the stability for uncertain discrete systems.Some discrete Jensen inequalities and free-weighting matrices are used to improve the conservativeness.Both linear fractional and nonlinear perturbations of systems are considered in this paper.Finally,a numerical example is provided to show the proposed result.