A quasi-two-dimensional physics-based model of HEMT transistor without using any smoothing functions for joining the linear and saturation regions of current-voltage (I-V) characteristics was developed. Considering the intervalley transitions of electrons and the presence of holes in the channel of transistor, we calculated the nonuniform spatial distributions of the electrical field, electron temperature, and electron mobility within the channel. The model is in a good agreement with experimental data over the linear and saturation regions of operation. The model provides precise simulating of HEMT transistors and can be utilized as a tool for analysis and prediction of influence of the material parameters on device and circuit characteristics.