This paper constructed a two-period overlapping generations (OLG) model to investigate the effects of the energy tax on environmental quality (the first dividend) and output level (the second dividend) to review the double dividend effect of the energy tax. According to the results of comparative static analysis, we found that the energy tax can improve environmental quality but cannot affect the output level. This suggests that the double effect of the energy tax is not supported in the OLG model. This is because an agent can only survive two periods, and need to give consideration to the consumption level of two-generation and the environmental quality of second-generation for pursuing the maximization of lifetime utility, therefore, the agent must maintain consumption (output) stability, and the double dividend effect does not exist.