Competitive sports are social sports activities with the main goal of winning competitions, which require athletes' physical and psychological abilities to be extremely high. Therefore, paying attention to the psychological health of outstanding athletes and improving their comprehensive quality are crucial to improving their sports performance. Traditional measures of psychological stress and anxiety mainly measure subjective stress feelings through stress perception scales, which ignores objective physiological indicators, while electroencephalogram (EEG), as an objective physiological data, has a strong correlation with different psycho-physiological conditions. Traditional feature extraction algorithms combined with machine learning require a large amount of a priori knowledge, while deep learning does not require a priori knowledge to deeply mine the deep features of the data. Therefore, this paper identifies and analyses psychological stress and anxiety in athletes based on deep learning by combining physiological data obtained from EEG signals and subjective data obtained from stress perception scales. Specifically, a stress EEG signal recognition model based on Transformer is proposed, the Transformer model in deep learning is explored, the encoder module in the Transformer model is applied to EEG signal analysis, and adaptive improvements are made and parameter optimization is carried out to be suitable for EEG signal analysis. Then experiments were carried out on two EEG signal public datasets, and the simulation experiment results proved the effectiveness of the proposed method.