We established an optimal combination of EEG recording during sparse multiband (MB) fMRI that preserves high-resolution, whole-brain fMRI coverage while enabling broad-band EEG recordings which are uncorrupted by MRI gradient artefacts (GAs). We first determined the safety of simultaneous EEG recording during MB fMRI. Application of MB factor = 4 produced <1°C peak heating of electrode/hardware during 20min of GE-EPI data acquisition. However, higher SAR sequences require specific safety testing, with greater heating observed using PCASL with MB factor = 4. Heating was greatest in the electrocardiogram channel, likely due to it possessing longest lead length. We investigated the effect of MB factor on the temporal signal-to-noise ratio for a range of GE-EPI sequences (varying MB factor and temporal interval between slice acquisitions). We found that, for our experimental purpose, the optimal acquisition was achieved with MB factor = 3, 3mm isotropic voxels, and 33 slices providing whole head coverage. This sequence afforded a 2.25s duration quiet period (without GAs) in every 3s TR. Using this sequence, we demonstrated the ability to record gamma frequency (55-80Hz) EEG oscillations, in response to right index finger abduction, that are usually obscured by GAs during continuous fMRI data acquisition. In this novel application of EEG-MB fMRI to a motor task, we observed a positive correlation between gamma and BOLD responses in bilateral motor regions. These findings support and extend previous work regarding coupling between neural and hemodynamic measures of brain activity in humans and showcase the utility of EEG-MB fMRI for future investigations.