Electron mobility in the conduction band of II-VI semiconductors ZnSe, CdTe, ZnTe, and CdSe was studied. Temperature dependence of mobility was calculated using the methodology based on density functional theory calculations of the electronic states, phonon modes, and electron-phonon coupling constants, along with Fourier-Wannier procedure for interpolation to a dense grid in momentum space. The mobilities obtained from calculations within generalized gradient approximation of density functional theory overestimate the experimental mobility several times. The calculation that used improved electronic band structure and high-frequency dielectric constants obtained using a hybrid functional lead to a very good agreement with experimental mobilities for most of the materials studied. It was also found that the Fröhlich model provides a reasonably good estimate of mobilities around room temperature where longitudinal optical phonons provide the dominant scattering mechanism, as expected for these direct gap materials where all relevant electronic states are in the vicinity of the Γ point. The results indicate as well that the long-ranged part of electron-phonon interaction fully determines the electron mobility in the materials studied. For this reason, the approach where only this part of electron-phonon interaction is calculated using the relevant analytical formulas allows for accurate calculation of mobility without the use of the interpolation procedure for electron-phonon coupling constants.