Currently many companies are looking for solutions to reduce carbon emissions associated with their operations in their supply chain. Operational adjustments, such as modifications in order quantities have proven to be an effective way to decrease carbon emissions in the supply chain. In this paper, we consider a single vendor single buyer supply chain problem where a single vendor manufactures finished goods at a finite rate in order to deliver finished goods to a single buyer. In the model, we introduce an integrated environmental inventory model under the cap-and-trade system incorporating the carbon emissions caused by logistics and warehousing activities. Also we derive the order quantity for finished goods and number of shipments between vendor and buyer and numerically examine the carbon trade and carbon cap on order quantity and number of shipments between vendor and buyer.