Because of the short-term diseconomies and externalities of low-carbon products, effective government intervention becomes a necessary tool for enterprises to produce low-carbon products. Under government regulation, a dynamic evolutionary game model is used for theoretical analysis. And the case data of new energy vehicle enterprises are used for simulation to explore the implementation effects of different punishment mechanisms on enterprises' production of low-carbon products. The results show that: (i) in the game between government and enterprises, consumers' green preferences, the differentiation between low-carbon products and high-carbon products, including the difference in cost and environmental friendliness, the market demand, and the purchase cost are important factors affecting game strategies. (ii) Under traditional regulatory, both the static and dynamic penalty mechanisms are favorable for enterprises to adopt the strategy of producing low-carbon products. What' more, the stronger the penalty, the faster the enterprises transform to produce low-carbon products. (iii) Under Internet regulatory, the strong dynamic penalty mechanism can better promote enterprises to produce low-carbon products, while the static penalty mechanism can't promote enterprises to produce low-carbon products effectively. On this basis, it is suggested that while regulating enterprises' production behavior, the government could also increase the demand for green consumption to pull enterprises to produce low-carbon products. In addition, it is suggested that the government's regulatory approach should be matched with the penalty mechanism, and the synergistic effect among regulatory instruments should be skillfully utilized, so as to promote the process of sustainable social development.