The electronic transport properties of graphene-based superlattice structures are investigated. A graphene-based modulation-doped superlattice structure geometry is proposed consisting of periodically arranged alternate layers: InAs/graphene/GaAs/graphene/GaSb. The undoped graphene/GaAs/graphene structure displays a relatively high conductance and enhanced mobilities at increased temperatures unlike the modulation-doped superlattice structure, which is more steady and less sensitive to temperature and the robust electrical tunable control on the screening length scale. The thermionic current density exhibits enhanced behavior due to the presence of metallic (graphene) monolayers in the superlattice structure. The proposed superlattice structure might be of great use for new types of wide-band energy gap quantum devices.