The calculations of the two-dimensional electron gas (2DEG) properties of pseudomorphic Al0.15Ga0.85N/AlN/GaN/(InyGa1-yN/GaN)MQW/Al0.15Ga0.85N/AlN/GaN heterostructures are presented. The effects of InGaN/GaN Multi-Quantum Wells (MQWs) on the band structures and carrier densities were investigated with the help of the one dimensional self-consistent solutions of the non-linear Schrodinger-Poisson equations. The 2DEG carrier density increased and the 2DEG carrier confinement improved by the insertion of InGaN/GaN MQWs into AlGaN/GaN HEMT structures. Also, we found that 2DEG carrier density of second subband significantly increased with In mole fraction in InGaN/GaN MQW for AlGaN/GaN HEMT structures. We proposed an optimized device structure using these findings. The 2DEG properties obtained via numerical calculations help to produce devices which have better electrical properties for further investigation. (C) 2014 Elsevier B.V. All rights reserved.