Surgical intervention in epilepsy aims to eliminate seizures in refractory patients by resecting the tissue responsible for seizure onset. Stereo-electroencephalography (sEEG) provides highly accurate but invasive electrophysiological measurements using narrow multi-contact electrodes implanted stereotactically through small holes in the skull. However, the three dimensional nature of sEEG measurements make observed seizure onsets difficult to associate with physical cortical regions. Three dimensional source localization from sEEG measurements can improve the interpretation of this data, but requires more accurate modeling as compared to localization from scalp EEG. Here, we present a finite difference approach that models the contact impedance and physical extent of each electrode (the so-called complete electrode model), to localize brain electrical activity from sEEG measurements. We applied this model to MRI and CT in a patient with intractable epilepsy, and reconstructed activity associated with multiple types of recurrent ictal spikes observed in sEEG. Independently, the neurosurgeon resected the clinically determined seizure focus, creating a resection cavity, and rendering the patient free of seizures. Our localization placed the seizure focus at a focal region in the occipital lobe, entirely contained within the resection region.