We report an automated morphological classification of galaxies into S-wise spirals, Z-wise spirals, and non-spirals using big image data taken from Subaru/Hyper Suprime-Cam (HSC) Survey and a convolutional neural network (CNN)-based deep learning technique. The HSC i-band images are about 36 times deeper than those from the Sloan Digital Sky Survey (SDSS) and have a two times higher spatial resolution, allowing us to identify substructures such as spiral arms and bars in galaxies at z>0.1. We train CNN classifiers by using HSC images of 1447 S-spirals, 1382 Z-spirals, and 51650 non-spirals. As the number of images in each class is unbalanced, we augment the data of spiral galaxies by horizontal flipping, rotation, and rescaling of images to make the numbers of three classes similar. The trained CNN models correctly classify 97.5 per cent of the validation data, which is not used for training. We apply the CNNs to HSC images of a half million galaxies with an i-band magnitude of i0.2, where we are hardly able to identify spiral arms in the SDSS images. Our attempt demonstrates that a combination of the HSC big data and CNNs has a large potential to classify various types of morphology such as bars, mergers, and strongly lensed objects.