The replacement of the AlGaN barrier layer of the AlGaN/GaN high electron mobility transistors (HEMTs) with InAlN of various In molar fractions is suggested. Internal polarization fields in the InAlN/(In)GaN quantum well are described using analytical formulae. InAlN/(In)GaN HEMTs quantum well free electron densities, transistor open channel drain currents and threshold voltages are calculated for different In molar fractions considering the maximal acceptable strain. It is suggested that 0.08 ≤ x ≤ 0.27 for a 15 nm thick InxAl1−xN barrier or 0 ≤ y ≤ 0.18 for a 5–10 nm thick InyGa1−yN channel can be applied for strain without layer relaxation while the quantum well free electron densities up to 4.6 × 1017 m−2 and the transistor open channel drain currents up to 4.5 A mm−1 can be expected.