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Most conventional methods to detect glottal closure instants (GCI) are based on signal processing technologies and different GCI candidate selection methods. This paper proposes a classification method to detect glottal closure instants from speech waveforms using convolutional neural network (CNN). The procedure is divided into two successive steps. Firstly, a low-pass filtered signal is computed, whose negative peaks are taken as candidates for GCI placement. Secondly, a CNN-based classification model determines for each peak whether it corresponds to a GCI or not. The method is compared with three existing GCI detection algorithms on two publicly available databases. For the proposed method, the detection accuracy in terms of F1-score is 98.23%. Additional experiment indicates that the model can perform better after trained with the speech data from the speakers who are the same as those in the test set.