Summary: A fuzzy regresion model illustrates the possibility of a considered system so that all given data are included in fuzzy intervals obtained by the model. So the fuzzy regression model is easily warped and bended by data with large error, when the error data are mixed in the possibilistic data. Especially the marginal data have the influence on configurating the shape of the model. Hyperelliptic functions are employed to select marginal data by means of recognizing data positions by adjusting its parameters. The fuzzy robust regression model is proposed in this paper so that the data with large error can be removed out of the marginal data using distance. As an application of the fuzzy robust regression model, the relation between economy in Asian region and environmental problem is analyzed. This application shows the meaning and effectiveness of the fuzzy robust regression model.