The article presents a gradual shift from the individual concept of data protection to the application of the group concept in the case of genetic data, which by its nature applies to more than one person. The application of the group concept is based on the norms of EU law, the case law of the European Court of Human Rights, the Court of Justice of the European Union, the Supreme Court of Iceland, as well as soft law documents. The jurisprudence presented in the paper argues that genetic information is relevant both to the donor of genetic material and to his relatives. Thus, the genetic data of person A created from a biological sample taken from him, may also constitute the genetic data of person B. Thus, the status of the data subject established under EU law should be extended to a larger number of persons than suggested by EU data protection legislation. The argumentation presented confirms the formation of indicating the group nature of genetic data. The continuous increase in the amount of genetic information in social and economic circulation will only reinforce this trend, which is aimed at the full realization of the right to personal data protection.