Presently, the environmental pollution problem, especially that of the small and medium-sized enterprises, has become a bottleneck restricting the high-quality development of China’s economy. It is imperative to accelerate the construction of a collaborative governance system with multiple subject participation. The behavior modes of Environmental Non-governmental Organizations (ENGOs), a key player in environmental care, in collaborating with core enterprises to control pollution from small and medium-sized suppliers should be explored. Therefore, we constructed a collaborative governance system consisting of ENGOs, focal firms and small and medium-sized suppliers. Then a two-stage game model was established to analyze the strategies of the governance system. Specifically, we studied the collaborative green cooperation strategy and antagonistic pressure supervision strategy between ENGOs and focal firms, analyzed factors influencing the strategic choices of each subject, and gave the advantages of the cooperation strategies through further comparisons. The results showed that: Under the cooperation strategy, ENGOs provided knowledge of environmental protection to the focal firms, then both the audit efforts of focal firms and the environmental protection efforts of small and medium-sized suppliers were effectively improved. Since ENGOs could not fully obtain the pollution information of small and medium-sized suppliers or accurately trace it from their downstream focal firms, it was difficult to drive the supply chain’s endogenous governance by this external monitoring of ENGOs, making the effect of pressure supervision strategy limited. The effectiveness of green cooperation strategy was positively correlated with the knowledge absorption capacity of focal firms, the unit product revenue, and the focal firms' violation penalties for small and medium-sized suppliers. When ENGOs' violation penalties for small and medium-sized suppliers were higher, or the reputation loss of focal firms was higher, more unfavorable conditions of green cooperation strategy could be achieved. Accordingly, ENGOs should choose to cooperate with focal firms with strong knowledge absorption ability and high profit per product; focal firms should learn environmental protection knowledge to improve the screening standards and review capabilities, and promote the achievement of green cooperation strategy conditions by strengthening active information disclosure; the government should promote the collaboration between ENGOs and focal firms by issuing environmental guidelines.