Afforestation projects are the main source of carbon sink. Measurement and impact analysis of carbon sink costs will help accelerate the marketization of forestry carbon sink. Considering the opportunity cost of land use and the carbon release cost of wood products, this study proposed a forestry carbon sink cost model under the Public–Private Partnership (PPP) and the direct (DI) investment mode based on the classic carbon sink model. Then, the proposed models were applied to a real-world afforestation project, the 20-year national afforestation project (NAP) in Laohekou City, Hubei Province, China. With the help of the input–output forestry carbon sink cost–benefit analysis framework, the dynamic analysis of factors such as rotation period, timber price, discount rate and yield rate for forestry is carried out. Results show that: (1) with the increasing of rotation period, wood market price, and wood yield rate, the carbon sink cost of Laohekou NAP gradually decreases, while the discount rate has the opposite trend; (2) the DI mode is more feasible than the PPP model at the present condition. The PPP mode is more feasible than the DI mode only when the wood price is lower than 73.18% of the current price, the yield rate is lower than 0.485, and the discount rate is higher than 6.77%. (3) When choosing tree species for NAP, the carbon sink capacity, wood market price, maturity time, and planting cost should be synthetically considered. The proposed model and the obtained results can not only support local governments and forestry carbon sink enterprises to make tradeoffs between PPP and DI mode, but also provide them with useful information for reducing carbon sink costs.