The most important goals included in the Europe 2020 Strategy are climate/energy targets, which determine not only the achievement of its other goals but also climate neutrality by 2050. This article aims to assess the efficiency of implementing the climate/energy targets of the Europe 2020 Strategy and to analyse changes over time, taking into consideration the structural diversity between the old (EU 15) and new EU members (EU 13) in the period of 2014−2018. The assessment of changes in the efficiency of climate/energy targets over time adds value to the evaluation methods used to date in this area. This was done using data envelopment analysis (DEA) and the Malmquist index. Earlier works usually specified only the level of target achievement, mostly jointly in relation to all of the goals of the Europe 2020 Strategy. The efficiency of their implementation at the macroeconomic level has not been studied. Furthermore, the added value of this paper consists in obtaining additional information concerning the internal structure and character of the studied efficiency of old and new member states. Changes in the efficiency level have been analysed with regard to the key climate/energy indicators used to monitor the Europe 2020 Strategy. Based on the results, the EU countries were divided into six groups with similar levels of efficiency in achieving energy and climate objectives and ranked using the DEA−Malmquist index according to changes in their level over time. This makes it possible not only to assess the performance of countries but also to formulate recommendations for decision-makers.