Through continuous feedback of the electroencephalogram (EEG) humans can learn how to shape their brain electrical activity in a desired direction. The technique is known as EEG biofeedback, or neurofeedback, and has been used since the late 1960s in research and clinical applications. A major limitation of neurofeedback relates to the limited information provided by a single or small number of electrodes placed on the scalp. We establish a method for extracting and feeding back intracranial current density and we carry out an experimental study to ascertain the ability of the participants to drive their own EEG power in a desired direction. To derive current density within the brain volume, we used the low-resolution electromagnetic tomography (LORETA). Six undergraduate students (three males, three females) underwent tomographic neurofeedback (based on 19 electrodes placed according to the 10-20 system) to enhance the current density power ratio between the frequency bands beta (16-20 Hz) and alpha (8-10 Hz). According to LORETA modeling, the region of interest corresponded to the Anterior Cingulate (cognitive division). The protocol was designed to improve the performance of the subjects on the dimension of sustained attention. Two hypotheses were tested: 1) that the beta/alpha current density power ratio increased over sessions and 2) that by the end of the training subjects acquired the ability of increasing that ratio at will. Both hypotheses received substantial experimental support in this study. This is the first application of an EEG inverse solution to neurofeedback. Possible applications of the technique include the treatment of epileptic foci, the rehabilitation of specific brain regions damaged as a consequence of traumatic brain injury and, in general, the training of any spatial specific cortical electrical activity. These findings may also have relevant consequences for the development of brain-computer interfaces.