This paper investigates the convergence of Hop-field neural networks with an event-triggered rule to reduce the frequency of the neuron output feedbacks. The output feedback of each neuron is based on the outputs of its neighbours at its latest triggering time and the next triggering time of this neuron is determined by a criterion based on its neighborhood information as well. It is proved that the Hopfield neural networks are completely stable under this event-triggered rule. The main technique of proof is to prove the finiteness of trajectory length by the Łojasiewicz inequality. The realization of this event-triggered rule is verified by the exclusion of Zeno behaviors. Numerical examples are provided to illustrate the theoretical results and present the goal-seeking capability of the networks. Our result can be easily extended to a large class of neural networks.