In this paper, we propose a unified physical model of InGaZnO [amorphous indium-gallium-zinc-oxide (a-IGZO)] thin-film transistors (TFTs) accounting for both charge injection at the contact and charge transport within the channel. We extract the current-voltage characteristics of the injecting contact from the measurements of a-IGZO TFTs fabricated on plastic foil. We show that the charge injection depends on both the drain and the gate voltages. We model the charge injection in staggered a-IGZO TFTs basing on the thermionic emission-diffusion theory including the charge carrier-dependent electron velocity due to the trap states in the subgap of the a-IGZO semiconductor. Combining the charge injection model with a charge transport model, we accurately and consistently describe the measurements of staggered a-IGZO TFTs with channel-length scaling from 200 μ m to 15 μ m. The proposed unified model is implemented in a circuit simulator and used to design unipolar inverters. The good agreement between simulations and measurements of the inverters further confirms the effectiveness of the proposed approach.