Density functional theory (DFT) calculations are carried out to study the structure and electronic structure of amorphous zinc oxide (a-ZnO). The models were prepared by the "melt-quench" method. The models are chemically ordered with some coordination defects. The effect of trivalent dopants in the structure and electronic properties of a-ZnO is investigated. Models of a-X 0.375 Z 0.625 O (X= Al, Ga and In) were also prepared by the "melt-quench" method. The trivalent dopants reduce the four-fold Zn and O, thereby introducing some coordination defects in the network. The dopants prefer to bond with O atom. The network topology is discussed in detail. Dopants reduce the gap in EDOS by producing defect states minimum while maintaining the extended nature of the conduction band edge.