Abstract: Recently, many image recognition applications employing convolutional neural networks have great success with satisfactory accuracy performances due to the rapid development of computer hardware and neural network technology. In these applications, convolutional neural networks used a group of rotated images in random angles from the same object as the network inputs during training to effectively recognize rotated objects. However, as shown in this study, this rotated-image approach could not effectively learn rotational features. In this paper, we present the multi-scale rotation-invariant features used in the convolutional neural network to identify rotational invariance. It can successfully capture rotational features for various data sets. Our model is established through the concepts of dihedral group transformations, multi-level, multi-scale, rotation-invariant pooling, and sharing weights of the convolutional neural network to learn convolution kernels that can achieve rotational invariance. Our model showed a significant improvement over other ones and practically learned the rotational invariance of an object.