The problem of event-triggered state estimation for a class of delayed recurrent neural networks with quantization is presented in this paper. In order to save the limited communication resource, a novel event-triggered scheme is constructed to determine whether or not the current sampled data should be transmitted to quantizer. A Luenberger-type state estimator is proposed based on incomplete measurements and a logarithmic quantizer is used to quantify the sampled data, which can reduce the data transmission rate in the network. Some delay-dependent sufficient conditions have been derived to ensure the existence of the desired estimator and the explicit expression of the Luenberger-type state estimator gain has been given. A numerical example is also given to show the effectiveness of the proposed method and the event-triggered estimation's capability of reducing the communication load.