To reveal the inteal physics of the low-temperature mobility of two-dimensional electron gas (2DEG) in AlGaN/GaN heterostructures, we present a theoretical study of the strong dependence of 2DEG mobility on Al content and thickness of AlGaN barrier layer. The theoretical results are compared with one of the highest measured of 2DEG mobility reported for AlGaN/GaN heterostructures. The 2DEG mobility is modelled as a combined effect of the scattering mechanisms including acoustic deformation-potential, piezoelectric, ionized background donor, surface donor, dislocation, alloy disorder and interface roughness scattering. The analyses of the individual scattering processes show that the dominant scattering mechanisms are the alloy disorder scattering and the interface roughness scattering at low temperatures. The variation of 2DEG mobility with the barrier layer parameters results mainly from the change of 2DEG density and distribution. It is suggested that in AlGaN/GaN samples with a high Al content or a thick AlGaN layer, the interface roughness scattering may restrict the 2DEG mobility significantly, for the AlGan/GaN interface roughness increases due to the stress accumulation in AlGaN layer.