(1) Background—Forest carbon sinks have the functions of emission reduction and poverty alleviation. In September 2020, China announced to increase the force of national independent contribution, and adopted more powerful policies and measures to strive reach the peak of carbon dioxide emissions by 2030 and achieve carbon neutrality by 2060. (2) Methods—Based on the forestry data from 1998 to 2018, the panel vector autoregression model (PVAR) was constructed, and the marginal carbon emission reduction cost ( carbon dioxide shadow price) was used as the proxy variable of forest carbon sink price. The long-term interaction between forest carbon sink and economic growth was analyzed from the perspective of economic value. (3) Results—According to PVAR estimates, firstly, economic growth has a significant positive effect on forest carbon sinks. After in-depth analysis, it is believed that economic growth promotes the development of forest carbon sinks may have the following reasons: ① Economic growth increases the investment in forest natural capital, that is, China's forestry ecological engineering, forest ecological benefit compensation system and a series of investment in forest natural capital increase forest carbon sinks. ② Economic growth has changed the consumption structure and industrial structure of forest products, because economic growth has transformed the demand structure of forest products from resource-based consumption to ecological consumption. At the same time, the forestry industry has gradually become advanced and rationalized under the traction of the change of consumption structure. ③ Economic growth promotes the transformation of forestry development mode, which makes China's forestry realize the transformation from ecological deficit to ecological surplus, and effectively protects forest resources. Secondly, forest carbon sinks have an inhibitory effect on economic growth. After in-depth analysis, forest carbon sinks inhibit economic growth may have the following reasons: ① National development strategy requires huge investment in forestry ecological construction. It needs a long period of investment recovery, but mainly requires social and ecological benefits, while economic benefits are difficult to highlight in a short time. ② The property rights of forest carbon sinks are not clear and the value measurement is unreasonable. The market function of forest carbon sinks cannot be effectively played, and it is difficult to transform the ecological value of forest carbon sinks into economic value on a large scale. From the perspective of property rights, forest carbon sink property rights have multiple attributes, and the definition is complex. In addition, natural risks and information asymmetry make forest carbon sink property rights have high risks, so that the arrangement of forest carbon sink property rights in China is unreasonable. From the perspective of value measurement, the demand power of forest carbon sinks under the Kyoto rule is insufficient, so that the mismatch between supply and demand cannot form an effective price and it is difficult to fully realize the function of resource allocation. (4) Conclusions and Discussions—Economic growth has a significant positive effect on forest carbon sinks, and forest carbon sinks have an inhibitory effect on economic growth. Based on the domestic and international situation, the Chinese government has made two major strategic plans to achieve emission peak and carbon neutrality. Achieving the goal of emission peak and carbon neutrality requires concerted efforts from all aspects of the socio-economic system. In the field of forestry, the path to achieve the goal of emission peak and carbon neutrality can be constructed from two aspects: changing land use patterns and increasing forest carbon sinks, so as to use land to achieve carbon sequestration and absorb CO2 through afforestation. This paper puts forward suggestions such as perfecting forest carbon sink trading platform, improving forest carbon sink pricing mechanism, reasonably defining forest carbon sink property rights and strengthening forest management, so as to realize the integrated development of forest carbon sink and economic growth. [ABSTRACT FROM AUTHOR]