This paper studied the event-triggered synchronization problem for time-delay neural networks under DoS attacks. A novel event-triggered scheme based on switching between periodic sampling and a continuous event-triggered scheme was proposed, which not only cuts down the number of data transmissions but also offsets cyberattacks. By choosing a suitable piecewise Lyapunov-Krasovskii functional and using several free-weighting matrices, sufficient conditions were established to ensure the exponential stability of the synchronization error system in the occurrence of DoS attacks. Furthermore, a co-design method was provided to acquire the desired non-fragile output-feedback control gain and event-triggering parameter. Finally, a numerical example was given to illustrate the usefulness of the proposed approach.