Channel-doped AlGaN/GaN heterostructure field-effect transistors (HFETs) with metal-insulator-semiconductor (MIS) structures have been fabricated to obtain the high drain current density and reduced gate leakage current. A thin bilayer dielectric of Al2O3(4 nm)/Si3N4(1 nm) was used as the gate insulator, to simultaneously take advantage of the high-quality interface between Si3N4 and AlGaN, and high resistivity and a high dielectric constant of Al2O3. A MIS HFET with a gate length of 1.5 μm has exhibited a record high drain current density of 1.87 A/mm at a gate voltage (Vg) of +3 V, which is ascribed to a high applicable Vg and a very high two-dimensional electron gas (2DEG) density of 2.6×1013 cm-2 in the doped channel. The gate leakage current was reduced by two or three orders of magnitude, compared with that in normal HFETs without a gate insulator. The transconductance (gm) was 168 mS/mm, which is high in the category of the MIS structure. Channel-doped MIS HFETs fabricated have thus been proved to exhibit the high current density, reduced gate leakage current, and relatively high transconductance, hence, promising for high-power applications.