A quaternary In0.04Al0.63Ga0.33N/GaN metal-insulator-semiconductor (MIS)-high electron mobility transistor (HEMT) on Si substrate using a GaN:C back-barrier (BB) layer and an AlGaN/AlN superlattice (SL) buffer layer to achieve a high breakdown voltage and a high output current density was demonstrated. Compared to the conventional device adopting AlGaN as the barrier layer, the proposed device showed a better 2DEG carrier density up to 1.9 x1013 cm-3, a higher output current density up to 1,070 mA/mm (improved by 47%), an on-resistance (Ron) as low as 7.64 Ω-mm (decreased by 26%), an off-state breakdown voltage up to 2,070 V, and an improved dynamic Ron performance (dynamic to static ratio increased to just 1.2 times at an applied drain-to-source stress voltage (VDS, stress) of 400 V). These results indicated the great potential of the InAlGaN/GaN MIS-HEMTs on Si for high-power switching applications.