We investigate the mechanism of charge transport in indium gallium zinc oxide (a-IGZO), an amorphous metal-oxide semiconductor. We measured the field-effect mobility and the Seebeck coefficient (S = Delta V/Delta T) of a-IGZO in thin-film transistors as a function of charge-carrier density for different temperatures. Using these transistors, we further employed a scanning Kelvin probe-based technique to determine the density of states of a-IGZO that is used as the basis for the modeling. After comparing two commonly used models, the band transport percolation model and a mobility edge model, we find that both cannot describe the full properties of the charge transport in the a-IGZO semiconductor. We, therefore, propose a model that extends the mobility edge model to allow for variable range hopping below the mobility edge. The extended mobility edge model gives a superior description of the experimental results. We show that the charge transport is dominated by variable range hopping below, rather than by bandlike transport above the mobility edge.