The variations of the electron mobility (mu) with electron temperature (T(e)), electric field (E) and drift velocity (upsilon(d)) for the 2DEG (2 Dimensional Electron Gas) channel of AlGaAs/GaAs HEMT (High Electron Mobility Transistor) have been investigated theoretically at low and moderate electric field regions. The results have been determined by using momentum and energy balance equations in the 2DEG at T(o)=1.7 K lattice temperature under zero magnetic field. The results enable us to predict the electron temperature and mobility at various electrical field regions, which are very important for understanding of the transport mechanisms, performance of HEMT and other devices. The theoretical results which are obtained by including the acoustic phonon and the polar optic phonon scattering mechanisms are compared with the available experimental results. A good agreement is observed at the low field region. However, the experimental and the theoretical results seem to deviate at the high electric field region, which indicates that additional scattering mechanisms should be taken into account.