This paper reports the material characteristics of In_0.66Ga_0.34As/In_yAl_1-yAs high electron mobility transistor （HEMT）. The linearly graded In_yAl_1-yAs buffer layer was grown on InP substrates by gas source molecular beam epitaxy （GSMBE）. The influence of In_yAl_1-yAs graded buffer layer with different thickness and different indium contents on the surface quality， the electron mobility and the concentrations of two-dimensional electron gas （2DEG） was studied. It was found that the electron mobility and concentration at 300 K （77 K） were 8570 cm²/（Vs）^-1 （23200 cm²/（Vs）^-1） and 3.255×10¹² cm^-2 （2.732×10¹² cm^-2）. The surface morphology of the material was also well improved and the root mean square （RMS） was 0.154 nm when the InAlAs graded buffer layer thickness was 50 nm. And this study can provide strong support for the improvement of HEMT performance.