Bilayer graphene nanoribbon (BGN) with tunable band gap which can be controlled by an external electric field is focused in our study. AB-stacked system with a stable structure is considered in a FET channel. Based on the assumed structure carrier density effect on charge mobility has been reported at different temperatures. Carrier mobility model is explained based on quantum confinement effect which indicates that carriers behave like traveling wave only in channel direction. Their behavior in other two directions can be approximated by standing wave as well. We prove that carrier mobility in BGNs is a function of temperature and carrier density which illustrate good agreement with experimental data.