The simultaneous application of functional MRI and EEG represents an attractive, non-invasive technique for the combined measurement of electrical and haemodynamic activity in the human brain. Simultaneous EEG/fMRI provides a brain imaging modality with millimeter spatial accuracy, and millisecond temporal resolution. However, simultaneously acquired measurements are difficult due to the artifacts that are induced in the EEG by both the temporally varying field gradients used in MRI, and also blood flow effects. In this paper we apply an EEG beamformer spatial filter to EEG data recorded simultaneously with fMRI. We show, using this technique, that it is possible to localise accurately electrical effects in the brain, and that the localisation of driven oscillatory responses in the human visual cortex are spatially co-incident with the fMRI BOLD response. We also show how the beamformer can be used to extract timecourses of electrical activity from areas of interest in the brain. Such timecourses have millisecond time resolution. Finally, we show that in addition to source localisation, the beamformer spatial filter acts to reject interference in EEG signals, thus increasing the effective signal to noise ratio of electrical measurements. We show that the EEG-beamformer can eliminate effectively the ballistocardiogram artifact as well as residual gradient artifacts that remain in EEG data following correction using averaged artifact subtraction techniques.