Defects and weak bonds generated in the fabricating process of amorphous InGaZnO(a-IGZO) films distribute non-uniformly in the band gap of the a-IGZO film in the form of traps. These traps would capture the charges induced by gate voltage, and affect the linear region mobility, channel carrier density and so on, then the electrical properties in the linear region of a-IGZO thin film transistor. The model used is based on the mobility in linear region which is in direct proportion to the ratio of the free charge to the total induced charge in the channel, and then the free charge and the trapped charge are separated. From the ratio of the density of free carriers to that of the trapped, a direct relationship with the derivative of the free charge with respect to surface potential, and the derivative of the trapped charge with respect to surface potential is calculated by bringing in the gate voltage that serves as an intermediate variable between the linear region mobility and the total induced charge. In this way, the free carrier density and the trapped carrier density can be separated by using the transfer characteristic and capacitor-voltage characteristic. Poisson's equation and Gauss theorem are applied to the interface between the channel layer and the insulating layer. In consideration of the non-uniform characteristic between the surface potential and the gate voltage, the relationship between the free carrier density and the surface potential, the trapped carrier density and the surface potential are obtained. Finally, the density of states in the linear region could be gained by differentiating the trapped carrier density with respect to surface potential.