Electron scattering rate and electron mobility limited by LO-phonons are calculated for a cylindrical polar semiconductor quantum wire with core-shell structure. Longitudinal optical phonons modes are developed within a dielectric continuum model. The influence of the thickness of the shell on the electron scattering rate by phonons is studied. Numerical calculations performed for a GaAs/AlGaAs quantum wire show that the electron–LO-phonon scattering rate changes with the thickness of the shell layer and is reduced considerably in the quantum wires having thicker shell, leading to higher electron mobility. The mobility can be improved up to several orders of magnitude.