In recent years, convolutional neural networks (CNNs) have shown great performance in various fields such as image classification, pattern recognition, and multi-media compression. Two of the feature properties, local connectivity and weight sharing, can reduce the number of parameters and increase processing speed during training and inference. However, as the dimension of data becomes higher and the CNN architecture becomes more complicated, the end-to-end approach or the combined manner of CNN is computationally intensive, which becomes limitation to CNN's further implementation. Therefore, it is necessary and urgent to implement CNN in a faster way. In this paper, we first summarize the acceleration methods that contribute to but not limited to CNN by reviewing a broad variety of research papers. We propose a taxonomy in terms of three levels, i.e.~structure level, algorithm level, and implementation level, for acceleration methods. We also analyze the acceleration methods in terms of CNN architecture compression, algorithm optimization, and hardware-based improvement. At last, we give a discussion on different perspectives of these acceleration and optimization methods within each level. The discussion shows that the methods in each level still have large exploration space. By incorporating such a wide range of disciplines, we expect to provide a comprehensive reference for researchers who are interested in CNN acceleration.