For a class of linear systems with norm-bounded uncertainty and interval time-varying delay, less conservative robust stability criteria is proposed based on the Lyapunov-Krasovskii(L-K) functional approach and linear matrix inequalitiy(LMI) technique. Firstly, the delay interval is partitioned into N equidistant subintervals and designing new L-K functional technique for each subinterval. Then, combined with a less conservative integral inequality, the time derivative of a candidate L-K functional is evaluated in each of these delay segments. Based on the convex combination technique, a new delay-dependent stability criteria for the system is formulated in terms of LMIs. Finally, numerical examples are given to show the effectiveness of the proposed approach.