More than 6 million cardiac arrests happen every year worldwide, which may cause the severe brain injury and seriously affect people's health. EEG can reflect the recovery of brain consciousness in cardiac arrest patients and assist neurophysiologists to give a reasonable prognosis. The goal of the George B. Moody Physionet/CinC Challenge 2023 is to predict the level of neurological recovery for cardiac arrest patients from longitudinal EEG recordings. In this paper, we proposed an approach to predict neurological outcome for cardiac arrest patients from long-term EEG by combing convolutional neural networks (CNNs) and a multi-scale Transformer. Firstly, convolutional neural networks are adopted to extract the small-scale patterns of brain activity from each 5 minutes EEG fragment. Secondly, the series of small-scale feature maps extracted by CNNs are encoded and fed into a multi-scale Transformer network to extract the long-term timing-dependencies of brain activity from different scales. Clinical data, such as age, sex, ROSC (return of spontaneous circulation), and OHCA (out-of-hospital cardiac arrest) etc. are concatenated into the feature vectors before the last fully connected layer. The proposed deep network framework adopts 18-channel EEG recordings as input, and the prediction probability of a poor outcome is output. Finally, a custom challenge loss and the cross-entropy loss are adopted to jointly optimize the proposed model. Our proposed model achieves the 5-fold cross-validation Challenge scores of 0.06, 0.23, 0.27, 0.34 for 12 hours, 24 hours, 48 hours, and 72 hours EEG recordings, respectively. Our team, MetaHeart_YNNU, achieves the Challenge scores of 0.05, 0.21, 0.22, 0.28 on the hidden validation set.