A new physics-based and computationally efficient drain current model for oxide semiconductor thin film transistors (TFTs) is developed. In this model, the influence of trap states in the band gap is taken into account to reproduce the gradual increase of the subthreshold current. Analytical expressions for the trapped electron densities are used to reduce the calculation time when solving the Poisson equation. The developed drain current model includes both drift and diffusion components, and it can thus be applied to the subthreshold, linear, and saturation regions. Calculations using the model produce results that are in good agreement with the measured drain current characteristics of amorphous indium gallium zinc oxide TFTs over a wide range of gate and drain voltages. The presented model is expected to play an important role in the analysis of TFT characteristics and the design of TFT structures to realize large-sized, high quality sheet-type displays with oxide semiconductor TFT backplanes.