Abstract: Based on endogenous growth model of human capital,carbon dioxide emissions are introduced into the model according to the relationship of energy and carbon dioxide emissions provided by IPCC, in addition, carbon dioxide is introduced into utility functionas the environmental quality. The optimal control theory is used to obtain the steady economic growth and the growth rate of carbon dioxide, and the conditions of achieving the double targets on economic growth and carbon dioxide emission reduction in the steady-state are analyzed. It is proved that human capital can overcome the decreasing marginal utility of physical capital and disutility of carbon dioxide emissions in order to achieve economic growth and carbon dioxide emission reduction. By comparing static analysis and parameter calibration, the changing trend of the growth rate in steady state is studied. The method of numerical simulation and phase diagram is used to examine the dynamic path and stability of system. Finally the constant quantity relation in steady state is simulated by parameter calibration method, proving the model conclusions.The inspiration of this paper includes three aspects:First, the consumption level of the whole society should be improved and the economic growth should be stimulated through consumption, rather than through saving investment; Second, the training of human capital should be strengthened and the overall quality of human capital should be improved, in order to make human capital become the new motive force and "new dividend" of China's economic growth; Third, the awareness of environmental protection and energy saving, as well as environmental legislation and environmental law enforcement should be strengthened.On the whole, the paper can help the researchers and the government to get the relationship of economic growth and carbon dioxide emissions and get the enlightenment that how to keep economic growth when reducing carbon dioxide emissions. Besides, the paper gives us a new perspective that we can research the relationship of economic growth and carbon dioxide emissions through endogenous economic model.

Key words: carbon dioxide emissions, human capital, endogenous growth model, steady state analysis, numerical simulation