In this paper, an analytical model for quantum confinement electron density in two-dimensional quantum well, has been investigated. In order to obtain the exact AlGaN/GaN HEMTs parameters such as electron density, the wave function, band gap, polarization charge, effective mass and dielectric constant, the hydrostatic pressure and temperature effects are taken into account. It has been found that the electron density decreases with increasing temperature and increases with increasing hydrostatic pressure. With increasing hydrostatic pressure, the effective mass decreases and the quantum confinement electrons are increased in the quantum well. Also with increasing hydrostatic pressure, the height of wave functions increase and decreases electron wave functions to penetrate the quantum barrier but increasing the temperature behaves the opposite of increasing the pressure. However, with increasing temperature, the effective mass is increased and the quantum confinement electrons are reduced. The calculated results for electron density are in good agreement with existing experimental data.