We developed a semi-analytical quasi-ballistic transport model for the nanowire metal-oxide-semiconductor field-effect transistors, dealing with finite lengths of source, channel, and drain. For the modeling, we used a combination of one-flux scattering matrices and analytical solutions of Boltzmann transport equations. The developed model was in quantitatively good agreement with numerical results, and well represented intermediate-scaled devices. In addition, we illustrated that the finite source seriously affect the distribution function of the carriers injected from the source, and the finite drain does for the backscattering into the channel from the drain. Finally, our model and results would help to understand physical aspects regarding quasi-ballistic transport in nanoscale devices.