Neurofeedback training is a form of brain training in which information about a neural measure is fed back to the trainee who is instructed to increase or decrease the value of that particular measure. This paper focuses on electroencephalography (EEG) neurofeedback in which the neural measures of interest are the brain oscillations. To date, the neural mechanisms that underlie successful neurofeedback training are still unexplained. Such an understanding would benefit researchers, funding agencies, clinicians, regulatory bodies, and insurance firms. Based on recent empirical work, an emerging theory couched firmly within computational neuroscience is proposed that advocates a critical role of the striatum in modulating EEG frequencies. The theory is implemented as a computer simulation of peak alpha upregulation, but in principle any frequency band at one or more electrode sites could be addressed. The simulation successfully learns to increase its peak alpha frequency and demonstrates the influence of threshold setting -the threshold that determines whether positive or negative feedback is provided. Analyses of the model suggest that neurofeedback can be likened to a search process that uses importance sampling to estimate the posterior probability distribution over striatal representational space, with each representation being associated with a distribution of values of the target EEG band. The model provides an important proof of concept to address pertinent methodological questions about how to understand and improve EEG neurofeedback success.