This article considers a two-echelon supply chain consisting of one large-size supplier and one small-size manufacturer. The supplier wholesales raw materials to the manufacturer who processes them into final products and sells them to consumers. The supplier also engages in Cournot competition with the manufacturer by producing its product and direct selling to consumers. In addition, as an energy service company, the supplier may choose low-carbon production for its product and may help the manufacturer to achieve low-carbon production by providing energy performance contracting services to the manufacturer. We investigate whom the supplier should provide energy performance contracting services to and analyze the impact of the unit matching cost and the investment cost coefficient in implementing the energy performance contracting project on the optimal decisions and profits for the two members. The results show that when the investment cost coefficient is not high, the supplier prefers to provide energy performance contracting services to the manufacturer under a low matching cost and to the two members under a high matching cost. However, the manufacturer prefers to enjoy energy performance contracting services for itself regardless of the matching cost. With the increasing investment cost coefficient, the supplier changes the decision to prefer to provide energy performance contracting services for itself. In such case, the manufacturer also prefers to not accept energy performance contracting services, so the two supply chain members’ profits are highest.