This paper studies sustainability of economic growth considering the risk of natural disasters caused by pollution in an endogenous growth model with physical and human capital accumulation. It is shown that economic growth is sustainable only if the tax rate on the polluting input is increased over time and that the long-term rate of economic growth follows an inverted V-shaped curve relative to the growth rate of the environmental tax. The social welfare is maximized under a positive steady-state growth in which faster accumulation of human capital compensates the productivity loss due to declining use of the polluting input.