This article explores the quasi-synchronization of discrete-time-delayed heterogeneous-coupled neural networks (CNNs) via hybrid impulsive control. By introducing an exponential decay function, two non-negative regions are introduced that are named time-triggering and event-triggering regions, respectively. The hybrid impulsive control is modeled by the dynamical location of Lyapunov functional in two regions. When the Lyapunov functional locates in the time-triggering region, the isolated neuron node releases impulses to corresponding nodes in a periodical manner. Whereas, when the trajectory locates in the event-triggering region, the event-triggered mechanism (ETM) is activated, and there are no impulses. Under the proposed hybrid impulsive control algorithm, sufficient conditions are derived for quasi-synchronization with a definite error convergence level. Compared with pure time-triggered impulsive control (TTIC), the proposed hybrid impulsive control method can effectively reduce the times of impulses and save communication resources on the premise of ensuring performance. Finally, an illustrative example is given to verify the validity of the proposed method.