This study proposes a novel Energy Efficiency Design Index (EEDI) estimation method considering the Onboard Carbon Capture and Storage (OCCS) system. The OCCS selectively captures and stores carbon dioxide (CO2) contained in exhaust gas emitted from the internal combustion engines of a ship. It also utilizes a CO2 capture process, a CO2 liquefaction process, and a CO2 storage tank. The status of greenhouse gas regulation for ships currently being discussed at the International Maritime Organization was investigated, and a modified EEDI estimation formula and a method for EEDI calculation considering the OCCS were evaluated. Case studies on a container feeder were conducted based on the proposed method in accordance with the EEDI regulations. The chemical absorption with an activated methyldiethanolamine solution was selected for the CO2 capture process. The captured CO2 was liquefied using cold energy from liquefied natural gas and ammonia. To improve the volume efficiency of the containment system, a prismatic pressure vessel was adopted for the CO2 storage tank. The results demonstrate that the required carbon capture ratio in the CO2 capture process is higher than the actual EEDI reduction rate.