We propose an approach of graph convolutional networks for robust infant cry classification. We construct non-fully connected graphs based on the similarities among the relevant nodes in both supervised and semi-supervised node classification with convolutional neural networks to consider the short-term and long-term effects of infant cry signals related to inner-class and inter-class messages. The approach captures the diversity of variations within infant cries, especially for limited training samples. The effectiveness of this approach is evaluated on Baby Chillanto Database and Baby2020 database. With as limited as 20% of labeled training data, our model outperforms that of CNN model with 80% labeled training data and the accuracy stably improves as the number of labeled training samples increases. The best results give significant improvements of 7.36% and 3.59% compared with the results of the CNN models on Baby Chillanto database and Baby2020 database respectively.