We propose a simulation model to explain two‐dimensional field‐effect operation of undoped poly‐Si thin‐film transistors (TFTs) under small drain voltages. Our model includes both thermionic‐emission and drift‐diffusion conduction processes. We calculated grain‐boundary potential barriers, channel currents, and various device parameters depending on grain size and defect density. In order to validate our model, we compared calculated currents with experimental data for two types of poly‐Si TFTs. We could obtain good current fits simultaneously in both subthreshold and linear regions by adopting proper densities of states in the poly‐Si channels. We could also explain well the temperature‐dependent current changes and the current activation energy versus the gate voltage. Finally, we succeeded in modeling the drain current under small drain voltages by using the combined transport process in the two‐dimensional grain‐boundary structure. ©1995 American Institute of Physics.