Abstract The k–ω model for turbulence was first proposed by Kolmogorov. A new k–ω model for stellar convection was developed by Li, which could reasonably describe turbulent convection not only in the convectively unstable zone, but also in the overshooting regions. We revised the k–ω model by improving several model assumptions (including the macro-length of turbulence, convective heat flux, and turbulent mixing diffusivity, etc.), making it applicable not only for convective envelopes, but also for convective cores. Eight parameters are introduced in the revised k–ω model. It should be noted that the Reynolds stress (turbulent pressure) is neglected in the equation of hydrostatic support. We applied it into solar models and 5 M ⊙ stellar models to calibrate the eight model parameters, as well as to investigate the effects of the convective overshooting on the Sun and intermediate mass stellar models.