While it is known that the charge-carrier mobility in organic semiconductors is only weakly dependent on the electric field at low fields, the experimental mobility in organic field-effect transistors using silylethynyl-substituted pentacene is found to be surprisingly field dependent at low source-drain fields. Corroborated by scanning Kelvin probe measurements, we explain this observation by the severe difference between local conductivities within grains and at grain boundaries. Redistribution of accumulated charges creates very strong local lateral fields in the latter regions. We further confirm this picture by verifying that the charge mobility in channels having no grain boundaries, made from the same organic semiconductor, is not significantly field dependent. We show that our model allows us to quantitatively model the source-drain field dependence of the mobility in polycrystalline organic transistors.