This article proposes a brain-inspired generative (BIG) model that merges an impulsive-attention neural network and a variational autoencoder (VAE) for identifying cognitive states based on electroencephalography (EEG) data. A hybrid learning method is presented for training the model by integrating gradient-based learning and heteroassociative memory. The BIG model is capable of achieving multi-task objectives: EEG classification, generating new EEG, and brain network interpretation, alleviating the limitations of excessive data training and high computational cost in conventional approaches. Experimental results on two public EEG datasets with different sampling rates demonstrate that the BIG model achieves a classification accuracy above 89\%, comparable with state-of-the-art methods, while reducing computational cost by nearly 11\% over the baseline EEGNet. Incorporating the generated EEG data for training, the BIG model exhibits comparative performance in a few-shot pattern. Ablation studies justify the poised brain-inspired characteristic regarding the impulsive-attention module and the hybrid learning method. Thanks to the performance advantages with interpretable outputs, this BIG model has application potential for building digital twins of the brain.