This study explores technology licensing in a low-carbon supply chain under cap-and-trade regulations, with an upstream firm holding partial shareholding in a downstream firm. We established a Stackelberg game to analyze four licensing strategies: free, fixed fee, royalty, and revenue-sharing. We investigate the effects of vertical shareholding and cap-and-trade regulation, as well as whether technology licensing yields a more favorable outcome compared to non-licensing and which licensing strategy proves superior. The findings reveal that when the upstream firm holds a higher share in the downstream firm, it results in increased profits for the upstream firm, the supply chain system, and consumer surplus, but decreased profit for the downstream firm. Furthermore, when carbon emission quotas are sufficiently high (low), a higher carbon trading price leads to increased (decreased) supply chain profitability, while inevitably decreasing consumer surplus. Increased carbon emission quotas consistently contribute to increased supply chain profitability, but have no impact on consumer surplus. All licensing contracts enhance the profitability of the upstream firm, the supply chain system, as well as consumer surplus, with revenue-sharing emerging as the most effective strategy. However, whether technology licensing promotes social welfare depends on factors such as the carbon emissions per unit of product and the environmental impact of each unit of carbon emission.