In this paper, the Numerov method is applied to solve the Schroedinger equation for $Al_{0.3}Ga_{0.7}AS/GaAs/Al_{0.3}Ga_{0.7}As$ double-heterojunction HEMT structures. The 3 subband energy levels, corresponding wave functions, 2-dimensional electron gas density, and conduction band edge profile are calculated from a self-consistent iterative solution of the Schroedinger equation and the Poisson equation. In addition, 2-dimensional electron gas densities in a quantum well of double heterostructure are calculated as a function of applied gate voltage. The density in the double heterojunction quantum well is increased to about more than 90%, however, the transconductance of the double heterostructure HEMT is not improved compared to that of the single heterostructure HEMT. Thus, double-heterojunction structures are expected to be suitable to increase the current capability in a HEMT device or a power HEMT structure.