In this paper, we present a theory of electron mobility in nanowire metal-oxide-semiconductor field-effect transistors (MOSFETs). Numerical approach consists of the Kubo-Greenwood formula and the self-consistent solution of the Schrodinger and Poisson equations for cylindrical gated nanowires. Phonons and surface roughness scatterings are treated in accordance with literature. Moreover, this paper focuses on nanowire MOSFETs using a high-k/metal gate stack. This configuration is chosen to be as close as possible to experimental investigations. The impact of trapped charges in the oxide, called remote Coulomb scattering, is modeled following the Kubo-Greenwood approach and accounting for screening effect. A comparison with experiment is performed for a single cylindrical nanowire with diameter of 20 nm. The diameter dependence is highlighted and it is shown that silicon thickness has a great impact on the mobility for diameters below 10 nm. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4719081]