Besides competition and cooperation, there also have neutrality relations, which is noncompetition and noncooperation, exists in Supply and Demand Network of Enterprises with Multi-function and Opening Characteristics (SDN). To reveal the evolution of cooperation, competition and neutrality relations among enterprises in SDN, an evolutionary model on node relations in SDN was build to solve the problem of real cooperative strategy selection. Base on evolutionary game theory, an enterprises relations evolutionary game model was established, and analyzed with numerical simulations in MATLAB. The results show that transferable and non-transferable incomes determined the choice of cooperation, competition and neutrality strategy. Opportunistic behavior and malicious competition exited in SDN, which reduced the overall revenue and destroyed the stability of SDN. Enhanced supervision and punishment in SDN will improve enterprises’ relations from neutrality to cooperation.