We present a model of the charge transport in thin film organic field-effect transistors with the active channel made of linear conjugated chains stacked on the substrate with end-on-orientation. The transport was simulated in a box consisting of 25 polymer chains, in which the delocalized quantum orbital eigenstates of the on-chain hole distribution were calculated. The inter-chain charge transfer was solved semi-classically. The full self-consistent distribution of charge density and electric field was determined for various applied gate and source-drain voltages. We found that the dependence of charge mobility on gate voltage is not monotonic: it first increases with increasing gate voltage for a limited interval of the latter, otherwise it decreases with the gate voltage. Next, we found formation of the second resonant peak for higher gate voltages. The mobility dependence on the gate voltage confirmed that the current flowing through the active semiconductor layer should be described not only as the hole transfer between adjacent repeat units of the neighbouring chains, but also as the transfer of coherences among on-chain repeat units. The presented model can also give a new insight into the charge transport in organic field-effect transistors with a novel vertical architecture.