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As the field of computational cognitive neuroscience continues to expand and generate new theories, there is a growing need for more advanced methods to test the hypothesis of brain-behavior relationships. Recent progress in Bayesian cognitive modeling has enabled the combination of neural and behavioral models into a single unifying framework. However, these approaches require manual feature extraction, and lack the capability to discover previously unknown neural features in more complex data. Consequently, this would hinder the expressiveness of the models. To address these challenges, we propose a Neurocognitive Variational Autoencoder (NCVA) to conjoin high-dimensional EEG with a cognitive model in both generative and predictive modeling analyses. Importantly, our NCVA enables both the prediction of EEG signals given behavioral data and the estimation of cognitive model parameters from EEG signals. This novel approach can allow for a more comprehensive understanding of the triplet relationship between behavior, brain activity, and cognitive processes.