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With the development of e-commerce and the increase of consumers’ green consciousness, more and more consumers purchase green products online. The frequent occurrence of the fake green product in online shopping has been harmful to the management and operation of the online market. In order to find the ways for the platform to supervise effectively green products quality problems, we consider the role of blockchain technology, the dynamic penalty mechanisms, the three strategy choices of seller, and the green awareness of consumers, and establish a supervision game model with the participation of online platform, online seller and consumer, which analyzes the equilibrium state of the three parties. The results show that (1) the level of the consumers’ green awareness, the compensation for green consumers, and the cost saved by non-green products are the critical factors to ensure the effectiveness of the platform punishment mechanism; (2) the combine effect of dynamic punishment and blockchain supervision can effectively and rapidly improve the quality of green products; (3) the improvement of consumers’ green awareness can drive sellers to sell green product, and makes the platform to strengthen the supervision of fake green products.