AlGaN/GaN high-mobility transistor (HEMT) has been attracting people’s attention and is proved to have satisfactory performance due to its related properties such as high break-down voltage, high saturation velocity, high frequency, etc. Molecular Beam Epitaxy (MBE) is one of the methods used for growth of high-quality AlGaN/GaN heterostructure with a two-dimensional electron gas (2DEG) in between. The high mobility of the 2DEGs, which is essential for ideal device performance, is determined by the charge density of the 2DEG. It is influenced by not only Al composition and AlGaN thickness, but also by dislocation density and the MBE background impurity. In order to achieve a high mobility, the relationship of mobility and 2DEG charge density is studied systematically on samples with various Al composition and AlGaN thickness grown by plasma-assisted MBE. Hall measurement is adopted for the measurement of 2DEG mobility and corresponding charge density. GaN bulk substrate and GaN template substrate with different dislocation densities are used for MBE growth as a comparison study on the influence of dislocation density. A gate control method is also explored on one specific sample with fixed dislocation density and background impurity to experimentally study the relationship of mobility and 2DEG density. Temperature-dependent Hall measurement is conducted to study transport property at low-temperature where the mobility is mainly limited by dislocation and background impurity rather than phonons. By analyzing the experimental data and comparing with theoretical calculations, the influence of dislocation density and background impurity is explained.