The manufacturing industry is a major source of greenhouse gas emissions (GHG). Additive manufacturing, owing to its multiple advantages, plays a critical role in innovating the current manufacturing industry, especially from a supply chain perspective. Currently, the majority of research on GHG emissions in the manufacturing industry is focused on traditional manufacturing, either single processes in the supply chain or specific case studies, indicating the lack of models on GHG emissions in additive manufacturing-enabled supply chain structures. In this work, a mathematical model is established to estimate the GHG emissions in both traditional manufacturing and additive manufacturing-enabled supply chains. To explore the advantages of additive manufacturing in terms of fast production and reduced or even eliminated the need for assembly and labor involvement, a unique integrated production-inventory-transportation structure is investigated in additive manufacturing case studies. The results indicate that a potential reduction of 26.43% of GHG emissions can be achieved by adopting the additive manufacturing technique in the supply chain. Also, the impacts of rush order rate, emission intensity, and vehicle GHG emission constant rate on the overall GHG emissions are investigated in the sensitivity analysis. Results indicate that a 20% variation in GHG emission intensity (the amount of CO2eq emissions caused by generating a unit of electricity) can lead to a 6.26% change in the total GHG emissions in additive manufacturing.