This article addresses the quantized sampled-data (QSD) synchronization for inertial neural networks (INNs) with heterogeneous time-varying delays, in which the sampled-data control and state quantization effect have been considered. By utilizing a proper variable substitution to transform the original system into a first-order differential system, choosing a new Lyapunov-Krasovskii functional (LKF) containing both the continuous terms and the discontinuous terms, and applying Jensen inequality and an improved reciprocally convex inequality to estimate the derivative of the LKF, the sufficient conditions for QSD synchronization for INNs are newly obtained in terms of linear matrix inequalities (LMIs), and the desired QSD controllers are designed by solving a set of LMIs. Finally, three numerical examples are provided to validate the effectiveness and benefit of the proposed results.