The exponential extended dissipativity for delayed discrete-time neural networks (DTNNs) is researched in this article. The considered time-varying delays have distinctly larger values in intermittent time periods (named as large delay periods (LDPs)) than other time periods. Firstly, the DTNN with LDPs is modeled as a switched system with two subsystems. Then, the definition of exponential extended dissipativity is proposed, which reflects the relationship between the extended dissipativity performance and exponential decay rate. By using the proposed definition, constructing an augmented switched Lyapunov functional with LDP-based terms and using inequalities to estimate its forward difference, the criterion for guaranteeing the DTNNs to be exponentially extended dissipative is obtained. Moreover, the corresponding stability condition is obtained when the external disturbance is zero. Finally, three numerical examples are given to demonstrate the merits of wider applications and less conservatism of the proposed methods.