This work investigates the protocol-based synchronization of inertial neural networks (INNs) with stochastic semi-Markovian jumping parameters and image encryption application. The semi-Markovian jumping process is adopted to characterize INNs under sudden complex changes. To conserve the limited available network bandwidth, an adaptive event-driven protocol (AEDP) is developed in the corresponding semi-Markovian jumping INNs (S-MJINNs), which not only reduces the amount of data transmission but also avoids the Zeno phenomenon. The objective is to construct an adaptive event-driven controller so that the drive and response systems maintain synchronous relationships. Based on the appropriate Lyapunov functional, integral inequality, and free weighting matrix, novel criteria are derived to realize the synchronization. Moreover, the desired adaptive event-driven controller is designed under a semi-Markovian jumping process. The proposed method is demonstrated through a numerical example and an image encryption process.