Forests have multifunctional roles. They not only increase forest carbon sinks through afforestation and management, but also indirectly realize multiple benefits of "economy + ecology + society". Therefore, we construct a multiple output-benefit system of forest carbon sinks based on the development of forest carbon sinks in provinces of China. This system is also able to distinguish the importance of forest carbon sinks from other outputs. For the efficiency evaluation of multi-level output systems, this paper constructs a cross-evaluation model based on evidential reasoning method, the original efficiency information by conducting efficiency evaluation before information fusion. Further, the spillover effects and influencing factors of forest carbon sink efficiency are analyzed through a spatial regression model to explore the spatial characteristics of forest carbon sink efficiency in China. The results show that: (1) there is a large gap between the cross-efficiency levels of forest carbon sinks in various regions of China, with significant spatial correlation. For the perspective of direct output benefits, the cross-efficiency of the eastern region is higher, while the cross-efficiency of the northwestern region is lower; for the perspective of indirect output benefits, the cross-efficiency of the southeastern region is higher. (2) China's forest carbon sink has a significant positive spillover effect, and the indirect output cross-efficiency has a significant negative impact on the forest carbon sink in its own region. Further analyzing the impact of indirect output cross-efficiency, it is found that the cross-efficiency of the ecological dimension and the cross-efficiency of the social dimension have a significant negative impact on the forest carbon sink in its own region, and the economic dimension has a significant positive impact on the forest carbon sink in its own region. In conclusion, corresponding policy recommendations are proposed for the development of forest carbon sinks to promote the realization of the dual-carbon goal.