The rapid development of the global economy has also caused the deterioration of the natural environment. The traditional economic growth method can no longer meet the development requirements of the times for the environment. The realization of sustainable and green development of human society has become the consensus of the whole society. To improve the degree of the greening of the economy, it is necessary to coordinate the management of various departments and to integrate the concept of environment and resources into economic growth. It is an important way for government departments to formulate corresponding sustainable green growth policies by relying on laws to achieve the strategic goals of sustainable green growth. In order to explore the role of government agencies in sustainable green growth through the enactment of relevant laws, this article takes China as the study of the environment. From the perspective of environmental protection tax law, through the establishment of the relationship model between ET and economic variables and ET and environmental indicators, using vector autoregression and system dynamics simulation analysis methods, the effect of ET on the environment and economy is studied. In the analysis of the impact on the environment, the impact of the auxiliary policy of ET on sustainable green growth is discussed. The experimental results show that the impact of environmental tax (ET) on GDP is more obvious. The simulation results show that when the proportion of technology investment is 35%, the promotion effect of sustainable green growth is the best. That is to say, the formulation of relevant laws and policies by government agencies has a certain role in promoting sustainable green growth.