Electroencephalogram (EEG) decoding remains a critical challenge in brain-computer interfaces (BCIs) due to the high-dimensional spatial complexity, task-dependent spectral variations, and non-stationary temporal dynamics of EEG signals. To address these challenges, we propose the state-space model (SSM)-Transformer-based dual-scale convolutional neural network (STDCNN), a novel hybrid architecture that integrates a dual-scale convolutional module, an SSM, and a Transformer module. The dual-scale convolutional module effectively captures spatial and spectral features at multiple scales, providing a rich representation of EEG signals. The SSM models dynamic temporal variations with linear-time complexity, offering efficient sequence processing. To compensate for the SSMs limited ability to capture long-range dependencies, the Transformer module applies self-attention to explicitly model global temporal relationships, thereby further enhancing the quality of temporal feature representations. Comprehensive evaluations across four EEG datasets, BCI-IV 2a and 2b (motor imagery tasks) datasets, SJUT emotion EEG dataset (SEED) (emotion recognition task), and a collected dataset (motor intention task), demonstrate STDCNN’s superior performance. STDCNN achieves state-of-the-art classification accuracy of 86.73% and 91.02% on the BCI-IV 2a and 2b datasets, respectively, 98.80% on the SEED dataset, and 92.06% on the collected dataset, significantly outperforming existing models. These results highlight STDCNN’s potential robust and scalable solution for high-performance EEG decoding in diverse BCI applications.