A complete model is proposed to analyze the electron density perturbation caused by tsunami-induced gravity waves. Loss mechanisms of thermal conduction, viscosity, and ion drag are considered in deriving the dispersion relation of the atmospheric gravity waves (AGWs). This model is then used to analyze the electron density perturbation in the ionosphere caused by the Sumatra tsunami on 26 December 2004. It is found that the AGWs move horizontally at the same speed with that of the tsunami and are trapped at about 400 km high. The simulation results well explain that about 13 min after the tsunami triggers AGWs, electron density perturbation in the ionosphere can be detected by satellites that pass over.