Radial core/shell nanowires (NWs) represent an important class of one-dimensional (1D) systems with substantial potential for exploring fundamental materials electronic and photonic properties. Here, we report the rational design and synthesis of InAs/InP core/shell NW heterostructures with quantum-confined, high-mobility electron carriers. Transmission electron microscopy studies revealed single-crystal InAs cores with epitaxial InP shells 2-3 nm in thickness, and energy-dispersive X-ray spectroscopy analysis further confirmed the composition of the designed heterostructure. Room-temperature electrical measurements on InAs/InP NW field-effect transistors (NWFETs) showed significant improvement in the on-current and transconductance compared to InAs NWFETs fabricated in parallel, with a room-temperature electron mobility, 11,500 cm(2)/Vs, substantially higher than other synthesized 1D nanostructures. In addition, NWFET devices configured with integral high dielectric constant gate oxide and top-gate structure yielded scaled on-currents up to 3.2 mA/microm, which are larger than values reported for other n-channel FETs. The design and realization of high electron mobility InAs/InP NWs extends our toolbox of nanoscale building blocks and opens up opportunities for fundamental and applied studies of quantum coherent transport and high-speed, low-power nanoelectronic circuits.