An analytical surface-potential-based drain current model for amorphous indium–gallium–zinc–oxide (a-InGaZnO) thin film transistors (TFTs) is proposed by introducing an effective charge density approach in this paper. This approach gives two initial approximate values of the effective state density and the effective thermal voltage by using the dominant state of the free charge density in total charge density, and then obtains a high-precision one-exponent equivalent transformation for three-exponent total charge density. Based on this approach, we have solved the problem that the physical meaning of the transition area in the regional method is not clear and a one-piece analytical surface potential solution to Poisson’s equation is successfully derived. Furthermore, the drain current is also explicitly derived from the charge sheet model and I-V characteristics of a-InGaZnO TFTs are reproduced from the above obtained model. Finally, accurate and effective surface-potential model and drain current model are obtained and verified by experimental data, respectively. Good verification results prove that the proposed model could become an accurate and suitable tool for being embedded into a circuit simulation.