<p>This study aims to provide insights of carbon emissions reduction considering carbon policies (the carbon tax policy and the cap-and-trade policy) and asymmetric information. The brand is often unaware of supplier’s ability of carbon abatement cost-control (ability) and his effort of carbon reduction. Therefore, the brand suffers from adverse selection and moral hazard of her supplier. We innovatively explore the impact of two-dimensional asymmetric information on carbon reduction incentives. And our study suggests that (1) The proportion of an incentive contract depends on the supplier’s degree of risk aversion as well as uncertainty about the ability of carbon abatement cost-control under two-dimensional asymmetric information. (2) The supplier’s efforts to reduce carbon emissions are hindered by his risk aversion. Furthermore, under two-dimensional asymmetric information, supplier’s efforts of weak ability to lower carbon emissions are exacerbated by uncertainty about his ability. (3) Interestingly, for profits of the brand under asymmetric information, the brand will gain more under some conditions. When the carbon trading market is inactive, the brand will benefit from the cap-and-trade policy. Instead, when the carbon trading market is active, the brand is more profitable under the carbon tax policy. For profits of the supplier under asymmetric information, they are raised by uncertainty about his ability. (4) Under the carbon tax policy, the extraction of consumer surplus is more advantageous in an asymmetric information environment when uncertainty about supplier’s ability is high. Previous papers that did not consider the interaction of supplier’s two-dimensional asymmetric information and carbon policies may have overestimated the scope for profitable carbon incentive of the brand. Our research enriches the literature on asymmetric information and carbon emission reduction in supply chains.</p>