We have developed a subgap density of states (DOS) model of amorphous In-Ga-Zn-O (a-IGZO) based on optical and electrical measurements. We study the optical absorption spectrum of the a-IGZO using UV-Vis spectroscopy. Together with the first-principles calculations and transient photoconductance spectroscopy from the literature, we determine that the valence band tail and deep-gap states are donors and can be described by exponential and Gaussian distributions, respectively. The conduction band tail and deep-gap states are examined using multi-frequency capacitance-voltage spectroscopy on a-IGZO thin-film transistors (TFTs). The extracted conduction band DOS are fitted to exponential (bandtail) and Gaussian (deep-gap) functions and their validity are supported by the activation energy vs. gate-source bias relationship of the a-IGZO TFT. The PL deep-level emission, which is almost identical to the conduction band deep-gap Gaussian, suggests that these states should be assigned as acceptors. The donor/acceptor assignments of subgap states are consistent with the 2D numerical TFT simulations.