Contemporary debates on the ethics of terrorism are mainly focused on the analysis of terrorist acts that began in the late twenty century or twenty-first century, ignoring or categorizing the anarchist wave of terrorism as “revolutionary terrorism”. The subject of this paper is the moral analysis of terrorism started by the anarchist from 1890 to 1920. The first part of the paper will analyze the theoretical basis of anarchism, in order to point out that anarchism is ideologically suitable for the use of political violence because it contains strong anti-state elements. In the second part of the paper, we will identify the main arguments for justifying terrorism in the anarchist movement, significant attention will be paid to the concept of "propaganda act" which is often cited as the main anarchist motivation for the acts of terrorism. In identifying moral rules, the paper will try to prove that anarchists used explicitly utilitarian arguments in justifying terrorism and that this kind of justification is not sufficient to justify terrorism by modern consequentialist standards and the moral principles set by just war theory. In the final part, we will support our hypothesis with a number of case studies that will include a moral evaluation of terrorist attacks carried out in France, Switzerland, Spain and the United States.