As a kind of non-invasive, low-cost, and readily available brain examination, EEG has attached significance to the means of clinical diagnosis of epilepsy. However, the reading of long-term EEG records has brought a heavy burden to neurologists and experts. Therefore, automatic EEG classification for epileptic patients plays an essential role in epilepsy diagnosis and treatment. This paper proposes an Attention Mechanism-based Wavelet Convolution Neural Network for epilepsy EEG classification. Attention Mechanism-based Wavelet Convolution Neural Network firstly uses multi-scale wavelet analysis to decompose the input EEGs to obtain their components in different frequency bands. Then, these decomposed multi-scale EEGs are input into the Convolution Neural Network with an attention mechanism for further feature extraction and classification. The proposed algorithm achieves 98.89% triple classification accuracy on the Bonn EEG database and 99.70% binary classification accuracy on the Bern-Barcelona EEG database. Our experiments prove that the proposed algorithm achieves a state-of-the-art classification effect on epilepsy EEG.