The worrying growth of global pollution from harmful combustion gases has prompted the world's largest industries to try to limit emissions of carbon dioxide as well as other greenhouse gases with new restrictions and rules. Such a trend has been considered by the International Maritime Organization (IMO) and the Marine Environment Protection Committee (MEPC) and from 2011 to 2013 established and implemented a new set of rules to be considered during the design and construction of new ships. Terms such as the Energy Efficiency Index (EEDI) and the Ship Energy Efficiency Management Plan (SEEMP) are introduced, and ships that meet all the new requirements are awarded the International Energy Efficiency Certificate (IEEC). Ships built before 2013 do not necessarily meet EEDI calculations, and therefore a comparison of the two ships based on their years of construction is made in this paper. The first ship, an example of a ship built before the introduction of the new rules, is the Toba supertanker built in 2004. The results of the Toba are compared to a crude oil and chemical tanker, the Panagia Thalassini, built in 2014 when new CO2 emission limits already had to be considered during construction. In addition to the analysis of the available literature, primarily related to the regulatory framework in the field of energy efficiency of ships, EEDI calculations for the above ships were conducted, as well as their comparison with the required value. The impact of individual quantities on the value of EEDI and the possibility of improving the project from the aspect of energy efficiency is presented.