This study explores the improvement of energy enterprises' efforts in green investment within the context of "Belt and Road" energy projects, focusing on addressing negative behaviors. The quantum game method is employed for this study. Firstly, a game model between financial institutions and energy enterprises is established. Secondly, we compare and analyze the set of game strategies and returns for both parties under different environments, including classical, separable quantum, and maximally entangled quantum environments. Subsequently, an entanglement contract is designed, and policy impacts are discussed through case analysis. The findings reveal that the promotion of energy enterprises' green investment behavior is most effective in the context of a maximally entangled quantum game. The signing of the "entanglement contract" enhances cooperation between the two parties, resulting in increased benefits for both sides as they increase their own efforts. This approach helps address the "prisoner's dilemma" problem arising from negative behaviors to a certain extent. Furthermore, the study suggests that government incentive policies or appropriate reduction of policy supervision can effectively encourage energy enterprises to adopt green investment behaviors. Hence, the proposal includes signing entanglement contracts, introducing incentive policies, and enhancing communication between the involved parties as strategies to foster positive green investment behavior in the context of "Belt and Road" energy projects.