For a class of discrete-time HOSNNs with time-varying delays, the global exponential synchronization problem and its application in audio encryption are addressed. A state feedback controller is designed to ensure the global exponential synchronization of response and drive discrete-time HOSNNs, and the controller gains are directly represented by the network parameters. Then, two numerical examples are given to demonstrate the applicability of the synchronization results. Moreover, a scheme to audio encryption/decryption is designed, and its applicability and safety analysis are tested by an interesting experimental simulation.