Electroencephalogram(EEG) is a test that detect brain activities using multiple electrodes placed on the scalp. Multiple channels of EEG signals are recorded through the electrodes and are widely used in applications such as neurological disease diagnosis, emotion recognition, and behavior modeling. Recently, deep learning methods have been applied to classify EEG signals, where the different EEG channels are almost treated as a 2D grid input to the machine learning model. This data formation doesn't consider The complex connection among the EEG channels is not considered in such data formation. In our work, we treat EEG signals as frames of graph, and propose an end-to-end edge-aware spatio-temporal graph convolutional neural network for EEG classification. Specifically, we iteratively apply graph convolutional layer spatially and standard convolutional layer temporally. Since there is no prior knowledge about the exact connection among EEG channels, in our model, we initialize the connection as complete graph and apply learnable mask to capture graph structure at different levels. Furthermore, we also propose an iterative method based on information aggregation in graph convolution mechanism to reveal the latent graph structure. Empirical evaluation shows that our model achieves superior performance over state-of-the-art methods for EEG classification, and the learnt and revealed latent EEG graph structure is verified to be meaningful by neuroscientists.