Inter-generational equity is essential for environmental sustainability. The current generation inherits an environment with a certain quality from the previous generation. The impact on the environment gradually exacerbates and accumulates over a period of time between two generations. However, currently there is no index available to assess inter-generational equity. Generally a typical environmental index is established to represent the environmental status in a specific year. This kind of index, although it presents the annual environmental variation, does not reflect the degree of change in environmental sustainability between two generations. Therefore, an inter-generational equity index (IGEI) and an endowment equation to examine the temporal trend of the changing environment are proposed for assessing inter-generational equity. To demonstrate the applicability of the endowment equation, an IGEI was established to assess the inter-generational equity of global warming. The global warming IGEI evaluates the status between two generations based on three sub-indexes; CO2 emission, loss due to climate disasters, and the size of the existing forest area. The pressure-state-response (PSR) framework was adopted to explain the causal relationship between these three sub-indexes. According to the endowment rate determined by the proposed equation for each sub-index, the increase in CO2 emission from 1980 to 2000 shows an obviously inequitable pattern between generations. Subsequently, the loss due to climate disasters between generations was also more serious. The size of the forest area, an important factor for reducing the impact of global warming, is unfortunately also decreasing significantly between generations. Using the endowment rate determined by the proposed endowment equation, the evaluation of the inter-generational equity is made possible and is demonstrated by the IGEI established for global warming.