Implementation of a carbon tax is one of the major ways to mitigate CO2 emission. However, blanket taxes applied to all industries in a country might not always be fair or successful in CO2 reduction. This study aims to evaluate the effects of carbon taxes on different industries, and meanwhile to find an optimal carbon tax scenario for Taiwan's petrochemical industry. A fuzzy goal programming approach, integrated with gray prediction and input–output theory, is used to construct a model for simulating the CO2 reduction capacities and economic impacts of three different tax scenarios. Results indicate that the up-stream industries show improved CO2 reduction while the down-stream industries fail to achieve their reduction targets. Moreover, under the same reduction target (i.e. return the CO2 emission amount to year 2000 level by 2020), scenario SWE induces less impact than FIN and EU on industrial GDP. This work provides a valuable approach for researches on model construction and CO2 reduction, since it applies the gray envelop prediction to determine the boundary values of the fuzzy goal programming model, and furthermore it can take the economic interaction among industries into consideration.