This paper studies the stability problem for discrete-time systems with interval time-varying delay. By dividing delay interval into two subintervals, a delay-dependent exponential stability criterion is obtained based on Lyapunov stability theory and reciprocally convex lemma. Furthermore, by assuming that the distribution of time-varying delay is known, the difference of Lyapunov functional is allowed to have positive upper bound for the value of time-varying delay in one subinterval, and a new delay distribution dependent stability criterion is obtained. The obtained result is also extended to cope with the robust delay distribution dependent stability problem for uncertain time-varying delay systems. All the obtained criteria are presented in terms of Linear Matrix Inequalities (LMIs). Finally one numerical example is given to show the effectiveness of the proposed method.