We introduce the Hexagonal Convolutional Neural Network (HCNN), a modified version of CNN that is robust against rotation. HCNN utilizes a hexagonal kernel and a multi-block structure that enjoys more degrees of rotation information sharing than standard convolution layers. Our structure is easy to use and does not affect the original tissue structure of the network. We achieve the complete rotational invariance on the recognition task of simple pattern images and demonstrate better performance on the recognition task of the rotated MNIST images, synthetic biomarker images and microscopic cell images than past methods, where the robustness to rotation matters.