Thermoelectric conversion is an energy harvesting technology that directly converts waste heat from various sources into electricity by the Seebeck effect of thermoelectric materials with a large thermopower (S), high electrical conductivity (σ), and low thermal conductivity (κ). State-of-the-art nanostructuring techniques that significantly reduce κ have realized high performance thermoelectric materials with a figure of merit (ZT= S²∙σ∙T∙κ⁻¹) between 1.5−2. Although the power factor (PF=S²∙σ) must also be enhanced to further improve ZT, the maximum PF remains near 1.5−4 mW m⁻¹ K⁻² due to the well-known trade-off relationship between S and σ. At a maximized PF, σ is much lower than the ideal value since impurity doping suppresses the carrier mobility. We prepared a metal-oxide-semiconductor high electron mobility transistor (MOS-HEMT) structure on an AlGaN/GaN heterostructure. Applying a gate electric field to the MOS-HEMT simultaneously modulates S and σ of the high-mobility electron gas from −490 μV K⁻¹ and ~10⁻¹ S cm⁻¹ to −90 μV K⁻¹ and ~10⁴ S cm⁻¹, while maintaining a high carrier mobility (~1500 cm² V⁻¹ s⁻¹). The maximized PF of the high-mobility electron gas is ~9 mW m⁻¹ K⁻², which is a two- to six-fold increase compared to state-of-the-art practical thermoelectric materials.