A fully analytical surface-potential-based drain current model for amorphous InGaZnO (α-IGZO) thin film transistors (TFTs) has been developed based on a Gaussian distribution of subgap states, with the central energy fixed at the conduction band edge, which is approximated by two exponential distributions. This model includes both drift and diffusion components to describe the drain current in all regions of operation. Using an empirical mobility relationship that depends on both horizontal and vertical electric field, it is demonstrated that the model describes accurately the experimental transfer and output characteristics, making the model suitable for the design of circuits using α-IGZO TFTs.