Economic and social progress is directly and closely related to energy consumption. In the latest decades, there is a higher need to reduce energy consumption from conventional sources, replacing it with energy obtained from unconventional sources. The environmental concern is one of the objectives of the European economic policy, with a particular focus on renewable energy consumption and energy efficiency in order to lower the environmental impact. In this context, we analyzed energy consumption per capita and renewable energy consumption per capita in the EU with the help of parametric methods, using the β-convergence model, and semiparametric methods, using the σ-convergence model. In this research we proposed to study six analysis models of the period 1960–2015, based on the availability of data. We concluded that the EU states went through a convergence process in a slow pace of energy consumption per capita and renewable energy per capita, showing a convergence pattern. The results of the study show that there is a relationship between the convergence of conventional energy consumption and the convergence of renewable (unconventional) energy consumption. The study covers a long period of time in which EU member states had different economic and social systems, implicitly different degrees and rates of development. In addition, the interest in renewable energy is relatively recent in the whole world. There is a possibility that future research will provide more optimistic results, in terms of accelerating the convergence rate, as appropriate measures and technologies are applied to renewable energy production in all EU member states.