We discuss the molecular beam epitaxial growth of the random alloy InAsSb for use as the channel in high electron mobility transistors (HEMTs). Room-temperature mobilities of 22 000 cm2/V s have been achieved at a sheet carrier density of 1.4×1012/cm2. This is a marked improvement over the mobility of 13 000 cm2/V s at the same carrier density obtained in previous attempts to grow the InAsSb channel using a digital alloy procedure [J. B. Boos, M. J. Yang, B. R. Bennett, D. Park, W. Kruppa, R. Bass, Electron. Lett. 35, 847 (1999)]. We have also implemented different barriers and buffer layers to enhance the transport properties and overall performance of the HEMT structure.