This paper proposes an automatic classification method to detect glaucoma in fundus images. The method is based on training a neural network using public image databases. The network used in this paper is the GoogLeNet, adapted for this proposal. The methodology was divided into two stages, namely: (1) detection of the region of interest (ROI); (2) image classification. We first used a sliding-window approach combined with the GoogLeNet network. This network was trained using manually extracted ROIs and other fundus image structures. Afterwards, another GoogLeNet model was trained using the previous resulting images. Then those images were used to train another GoogLeNet model to automatically detect glaucoma. To prevent overfitting, data augmentation techniques were used on smaller databases. The results demonstrated that the network had a good accuracy, even with poor quality images found in some databases or generated by the data augmentation algorithm.