Motor imagery (MI) has emerged as a classical paradigm in brain-computer interface (BCI) research. In recent years, advancements in deep learning techniques, such as the application of Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs), have enabled the use of MI classification. Despite their success, CNNs and RNNs are not capable of effectively extracting brain spatial and temporal information necessary for MI classification. Additionally, differences in individual subjects further complicate the classification process. To address these limitations, a novel Spatial-Temporal Transformer based on Domain Generalization (ST-DG) has been proposed for MI classification using EEG signals. This framework utilizes a spatial-temporal transformer architecture to capture essential spatiotemporal characteristics of the brain, while also employing Domain Generalization techniques to account for cross-subject variability and improve the model's generalization performance. Experimental results on two public datasets demonstrate the state-of-the-art classification performance.