Electroencephalography (EEG) plays a vital role in detecting how brain responses to different stimulus. In this paper, we propose a novel Shallow-Deep Attention-based Network (SDANet) to classify the correct auditory stimulus evoking the EEG signal. It adopts the Attention-based Correlation Module (ACM) to discover the connection between auditory speech and EEG from global aspect, and the Shallow-Deep Similarity Classification Module (SDSCM) to decide the classification result via the embeddings learned from the shallow and deep layers. Moreover, various training strategies and data augmentation are used to boost the model robustness. Experiments are conducted on the dataset provided by Auditory EEG challenge (ICASSP Signal Processing Grand Challenge 2023). Results show that the proposed model has a significant gain over the baseline on the match-mismatch track.