Mental arithmetic is a skill commonly used in daily life. It involves various cognitive processing processes that cause changes in brain activity， so research on its electroencephalogram （EEG） can help improve the level of research on cognitive tasks. Amplitude permutation entropy for global graph （APEGG） is proposed to apply to the study of EEG mental arithmetic， to make up that the traditional permutation entropy for graph （PEG） can not fully reflect changes of the neighboring nodes around brain network nodes， and overcome the problem of insensitive EEG signal amplitude. At first， the EEG brain network is constructed using the phase locking value （PLV）， the synchronization and correlation between multi-lead EEG signals are analyzed， and then the amplitude permutation entropy for global graph of the brain network at different frequency bands is calculated. Finally， support vector machine （SVM） is used for classification. EEG in public data sets is used for simulation， and the mental state of different frequency bands and resting state entropy scatterplot are analyzed， showing a larger difference. The classification results show better results compared with other algorithms.