Since dual channel supply chain has become one of the main modes of supply chain, its research has acquired great significance. This paper constructs a low-carbon dual channel supply chain composed of one manufacturer and one retailer. The manufacturer produces low-carbon product and high carbon product with substitution relationship. The retailer sells high carbon product in traditional channel. The manufacturer also sells low-carbon product in direct channel. The government, manufacturer and retailer conduct a three-level Stackelberg game. This paper studies the optimal decisions of the government, manufacturer and retailer under the three modes of carbon tax + subsidy, carbon tax only and subsidy only. It has been found that for social welfare, the carbon tax + subsidy model is higher than the subsidy model and carbon tax model. For manufacturer profit, the subsidy mode is the highest, followed by the carbon tax + subsidy mode. For retailer profit, the carbon tax + subsidy model is equal to the carbon tax model. The increase in the proportion of consumers who prefer high carbon product in the total market or product cost of low-carbon product, will increase the profit of traditional channel and reduce the profit of direct channel.