InAlN can be in-plane lattice matched (LM) to GaN, and the formed InAlN/GaN heterostructure is one kind of materials with high conductivity to be used in GaN-based high electron mobility transistors (HEMTs). It is reported that the high-mobility InAlN/GaN material is grown by using pulsed metal organic chemical vapor deposition (PMOCVD) on sapphire, and the Hall electron mobility reaches 949 and 2032 cm2/Vs at room temperature and 77 K, respectively. The two-dimensional electron gas (2DEG) is formed in the sample. When 1.2 nm thick AlN space layer is inserted to form InAlN/AlN/GaN structure, the Hall electron mobility increases to 1437 and 5308 cm2/Vs at room temperature and 77 K, respectively. It is shown by analyzing the results of X-ray diffraction and atomic force microscopy and the features of PMOCVD that the crystal quality of InAlN/GaN material is quite high, and the InAlN layer LM to GaN has smooth surface and interface. The high mobility characteristics of InAlN/GaN and InAlN/AlN/GaN materials are ascribed to the fact that the 2DEG has a comparatively low sheet density (1.61013-1.81013 cm-2), the alloy disorder scattering is weakened in the high-quality InAlN crystal since its compositions are evenly distributed, and the interface roughness scattering is alleviated at the smooth interface where the 2DEG is located.