This paper focuses on stability analysis and stabilization of nonlinear systems with interval time-varying delay, modeled by Takagi-Sugeno (T-S) fuzzy approach. To achieve more relaxation in the feasibility region, delay-partitioning approach is used for all integral terms in the Lyapunov-Krasovskii functional (LKF). A fuzzy Lyapunov function is proposed instead of non-integral term in LKF, and moreover, some slack matrices variables are offered to enlarge the design space. By doing this, new delay-dependent stability criteria are obtained. During the derivation of stability conditions, Jensen's integral inequality is applied to deal with integral terms. Furthermore, in this paper the problem of controller design via the parallel distributed compensation (PDC) scheme is studied. Stability and stabilization conditions with less conservative are achieved in terms of linear matrix inequality (LMI). Finally, two numerical examples are presented to show the effectiveness of the proposed results.