<p>This paper introduces the modified free-matrix-based integral inequality (MFBII) and investigates its application in the stability analysis of delayed neural networks through the Lyapunov-Krasovskii functional (LKF) approach. In order to provide a less conservative stability criterion, the MFBII is employed with an augmented vector that contains the derivative of the system state and the nonlinear function output. A corresponding double integral of the quadratic terms related to the augmented vector is newly constructed to utilize cross-information between components in the augmented vector. Two numerical examples demonstrate the effectiveness of the proposed method.</p>