Abstract: With the intensification of global warming and the increasing awareness of environmental protection, low-carbon economy and sustainable development have become a global consensus. As an important area of energy consumption and carbon emissions, supply chain management plays a key role in driving the green and low-carbon transition. Following Apple's Supplier Energy Efficiency Program, this paper considers a low-carbon retailer-led supply chain consisting of a retailer and supplier. We establish a two- period Stackelberg model without low-carbon incentive and a low-carbon incentive model with two different game mechanisms (one-period and two-period Stackelberg models), and compare the relevant results with an existing biform game mechanism for low-carbon technology (LCT) investment. Then, the supplier's investment behavior in LCT and the retailer's cost sharing behavior under different game mechanisms are discussed and analyzed. Analytic results show that, 1) The cost-sharing behavior of retailer in LCT investment is conducive to a “win-win” outcome; 2) Retailer always prefer to carry out decision-making behavior under the one-period Stackelberg game mechanism, and it can motivate suppliers to choose the one-period Stackelberg game mechanism through side-payment to achieve a win-win outcome; 3) Supplier can achieve a higher level of low-carbon technology under the biform game mechanism; 4) From the perspective of supply chain system profit, both one-stage Stackelberg game and biform game mechanisms are superior to two-stage Stackelberg game mechanism. This study can provide theoretical methods for production and operation management in the low-carbon supply chain, and make a new way for double carbon goals of achieving carbon peak, carbon neutral.