This paper researches the problem of stability analysis for distributed time-delay systems. A newly augmented Lyapunov-Krasovskii functional (LKF) is first introduced via a generalized delay partitioning approach. Then, a less conservative stability criterion is derived by introducing a novel Jensen inequality to estimate the integral terms in the derivative of LKF. The stability condition is given in terms of linear matrix inequality. Finally, the merits of the obtained stability criterion is shown by a well-known example.